To test the claim that the sample is from a population with a standard deviation less than 0.0390 g, and using a 0.05 significance level and a parametric method, certain requirements must be satisfied. The requirements include:
A. Either or both of these conditions are satisfied:
A. the population is normally distributed or the sample size is greater than 30.
C. The sample is a simple random sample.
The normality requirement for a hypothesis test of a claim about a standard deviation differs from the normality requirement for a hypothesis test of a claim about a mean. For a hypothesis test of a claim about a standard deviation, it is not necessary for the population to be normally distributed. Instead, either the population should be normally distributed or the sample size should be sufficiently large (typically greater than 30) for the Central Limit Theorem to apply. In this case, the requirement is satisfied if either the population is normally distributed or the sample size is greater than 30. However, the sample should still be a simple random sample, which ensures that the observations are independent and representative of the population.
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A sample of 18 male students was asked how much they spent on textbooks this semester. The sample variance was s2M = 35.05. A sample of eight female students was asked the same question, and the sample variance was s2F = 18.40. (Data collected by Megan Damron and Spencer Solomon, 2009.) Assume that the amount spent on textbooks is normally distributed for both the populations of male students and of female students.
a. Calculate a 90% confidence interval estimate for sigma2M, the population variance of the amount spent on textbooks by male students.
b. Calculate a 90% con?dence interval estimate for sigma2M, the population variance of the amount spent on textbooks by female students.
a.0.05 ≤ P (χ²(17) < (18 - 1)35.05/σ²M < χ²(0.95)(17))0.05 ≤ P (χ²(17) < 577.57/σ²M < χ²(0.95)(17))0.05 ≤ P (χ²(17) < 577.57/σ²M < 28.412)The above inequality represents the 90%
b. 0.05 ≤ P (χ²(7) < (8 - 1)18.40/σ²F < χ²(0.95)(7))0.05 ≤ P (χ²(7) < 122.18/σ²F < χ²(0.95)(7))0.05 ≤ P (χ²(7) < 122.18/σ²F < 14.067)
The above inequality represents the 90% confidence interval estimate for sigma2F.
a. 90% confidence interval estimate for sigma2M:We are given that the sample variance is s²M=35.05 and a sample of 18 male students was asked how much they spent on textbooks. We are also given that the amount spent on textbooks is normally distributed for both the populations of male students.
Using the Chi-Square distribution, we have: (n - 1)s²M/σ²M follows a Chi-Square distribution with n - 1 degrees of freedom.
Then, (n - 1)s²M/σ²M ~ χ²(n - 1)For a 90% confidence interval estimate, we can write: 0.05 ≤ P (χ²(17) < (n - 1)s²M/σ²M < χ²(0.95)(17))
Using the table of chi-square values with (n - 1) degrees of freedom, we have:χ²(0.05)(17) = 8.567χ²(0.95)(17) = 28.412
Substituting the values, we have:0.05 ≤ P (χ²(17) < (18 - 1)35.05/σ²M < χ²(0.95)(17))0.05 ≤ P (χ²(17) < 577.57/σ²M < χ²(0.95)(17))0.05 ≤ P (χ²(17) < 577.57/σ²M < 28.412)The above inequality represents the 90%
b. confidence interval estimate for sigma2M.b. 90% con? dence interval estimate for sigma2F:Using the same concept as above, we can write: 0.05 ≤ P (χ²(7) < (n - 1)s²F/σ²F < χ²(0.95)(7))
Using the table of chi-square values with (n - 1) degrees of freedom, we have:χ²(0.05)(7) = 3.357χ²(0.95)(7) = 14.067
Substituting the values, we have:0.05 ≤ P (χ²(7) < (8 - 1)18.40/σ²F < χ²(0.95)(7))0.05 ≤ P (χ²(7) < 122.18/σ²F < χ²(0.95)(7))0.05 ≤ P (χ²(7) < 122.18/σ²F < 14.067)
The above inequality represents the 90% confidence interval estimate for sigma2F.
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To calculate a 90% confidence interval estimate for σ2M, the population variance of the amount spent on textbooks by male students, we use the formula below:
[tex]$$\chi_{0.05,17}^2 <\frac{(n - 1)s^2}{\sigma^2} < \chi_{0.95,17}^2$$[/tex]
where n = 18, s2M = 35.05, df = n - 1 = 17, and χα2,
df is the critical value from the chi-squared distribution with df degrees of freedom.
We know that:
[tex]$$\chi_{0.05,17}^2 = 8.909$$[/tex]
and
[tex]$$\chi_{0.95,17}^2 = 31.410$$[/tex]
Substituting these values, we have:
[tex]$$8.909 < \frac{(18-1)(35.05)}{\sigma^2} < 31.410$$[/tex]
Solving for σ2, we have:
[tex]$$\frac{(18-1)(35.05)}{31.410} < \sigma^2 < \frac{(18-1)(35.05)}{8.909}$$[/tex]
Hence, a 90% confidence interval estimate for σ2M is:
[tex]$$(48.704, 194.154)$$b.[/tex]
To calculate a 90% confidence interval estimate for σ2F, the population variance of the amount spent on textbooks by female students, we use the formula below:
[tex]$$\chi_{0.05,7}^2 <\frac{(n - 1)s^2}{\sigma^2} < \chi_{0.95,7}^2$$[/tex]
where n = 8, s2F = 18.40, df = n - 1 = 7, and χα2,
df is the critical value from the chi-squared distribution with df degrees of freedom.
We know that:
[tex]$$\chi_{0.05,7}^2 = 14.067$$[/tex] and
[tex]$$\chi_{0.95,7}^2 = 2.998$$[/tex]
Substituting these values, we have:
[tex]$$14.067 < \frac{(8-1)(18.40)}{\sigma^2} < 2.998$$[/tex]
Solving for σ2, we have:
[tex]$$\frac{(8-1)(18.40)}{2.998} < \sigma^2 < \frac{(8-1)(18.40)}{14.067}$$[/tex]
Hence, a 90% confidence interval estimate for σ2F is:
[tex]$$(7.176, 23.622)$$[/tex]
Therefore, the 90% confidence interval estimate for σ2M,
the population variance of the amount spent on textbooks by male students, is (48.704, 194.154), while the 90% confidence interval estimate for σ2F,
the population variance of the amount spent on textbooks by female students, is (7.176, 23.622).
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Need help in proving theorems of square please ASAP
Answer:
The length of [tex]\overline{JO}[/tex] is 48.
Step-by-step explanation:
A square is a quadrilateral whose four sides have the same length and four internal angles have the same measure. The sum of measures of internal angles in quadrilaterals equals 360°. Let [tex]m\,\angle BOJ = 4\cdot x -6[/tex] and [tex]BO = 2\cdot x - 8[/tex], the value of [tex]x[/tex] is:
[tex]4\cdot (4\cdot x - 6) = 360^{\circ}[/tex]
[tex]16\cdot x -24 = 360^{\circ}[/tex]
[tex]16\cdot x = 384^{\circ}[/tex]
[tex]x = 24[/tex]
And the length of [tex]JO[/tex] is:
[tex]JO = BO = 2\cdot x - 8[/tex]
[tex]JO = 40[/tex]
The length of [tex]\overline{JO}[/tex] is 48.
reverse the order of integration and then evaluate the integral.
₀∫¹₄ᵧ∫⁴ x⁴eˣ^²ʸ dx dy
a. e¹⁶ - 1
b. e¹⁶ - 68/3
c. 4e¹⁶-68 / 3
d. 4e¹⁶ - 68
The correct answer is option (b): [tex]e^16 - 68/3[/tex]. The approximate value of this expression is [tex]e^16 - 68/3[/tex].
To reverse the order of integration, we need to change the order of integration and rewrite the limits of integration accordingly.
The given integral is:
∫₀¹₄ ᵧ ∫⁴ x⁴e^(x²ʸ) dx dy
To reverse the order of integration, we integrate with respect to y first. The limits of integration for y are 0 to 14ᵧ. The limits of integration for x will depend on the value of y.
∫₀¹₄ ᵧ ∫⁴ x⁴e^(x²ʸ) dx dy
Let's integrate with respect to x first:
∫⁴ x⁴e^(x²ʸ) dx = [1/5 x⁵e^(x²ʸ)]⁴₀
Now we can rewrite the integral with reversed order of integration:
∫₀¹₄ dy ∫⁴₀ x⁴e^(x²ʸ) dx
Plugging in the limits of integration for x:
∫₀¹₄ dy [1/5 x⁵e^(x²ʸ)]⁴₀
Now we can evaluate the integral:
∫₀¹₄ dy [1/5 (⁴)⁵e^(⁴²ʸ) - 1/5 (⁰)⁵e^(⁰²ʸ)]
Simplifying:
∫₀¹₄ dy [1/5 (1024e^(16ʸ) - 1)]
Now integrate with respect to y:
[1/5 (1024e^(16ʸ) - 1)]¹₄
Plugging in the limits of integration for y:
[1/5 (1024e^(1614) - 1)] - [1/5 (1024e^(160) - 1)]
Simplifying:
[1/5 (1024e^(224) - 1)] - [1/5 (1024e^(0) - 1)]
[1/5 (1024e^(224) - 1)] - [1/5 (1024 - 1)]
[1/5 (1024e^(224) - 1)] - [1/5 (1023)]
[1/5 (1024e^(224) - 1)] - [204.6]
To evaluate the expression, we need the actual numerical value for e^(224). Using a calculator, we find that e^(224) is an extremely large number. Therefore, we can approximate it as e^(224) ≈ 2.4858 x 10^97.
Plugging in the value:
[1/5 (1024 x (2.4858 x 10^97) - 1)] - [204.6]
Simplifying the expression:
[2.4858 x 10^97 - 1] / 5 - 204.6
The approximate value of this expression is:
e^16 - 68/3
Therefore, the correct answer is option (b): e^16 - 68/3.
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Suppose that you are testing the hypotheses H_o: μ = 82 vs. H_A: µ≠ 82. A sample of size 51 results in a sample mean of 87 and a sample standard deviation of 1.4.
a) What is the standard error of the mean?
b) What is the critical value of t^* for a 99% confidence interval?
c) Construct a 99% confidence interval for µ.
d) Based on the confidence interval, at α = 0.010 can you reject H_o? Explain.
The standard error of the mean is____ (Round to four decimal places as needed.)
a) The standard error of the mean can be calculated using the formula:
standard error = sample standard deviation / √(sample size).
Given a sample size (n) of 51 and a sample standard deviation (s) of 1.4, we can compute the standard error as follows:
Standard error = 1.4 / √51 ≈ 0.1967 (rounded to four decimal places).
b) To find the critical value of t^* for a 99% confidence interval, we need to consider the degrees of freedom. Since we have a sample size of 51, the degrees of freedom is n-1 = 51-1 = 50. Using a t-distribution table or calculator, the critical value for a 99% confidence interval with 50 degrees of freedom is approximately ±2.680.
c) To construct a 99% confidence interval for µ, we can use the formula:
Confidence interval = sample mean ± (critical value * standard error).
Using the given sample mean of 87 and the standard error calculated in part a, the confidence interval can be calculated as follows:
Confidence interval = 87 ± (2.680 * 0.1967) ≈ 87 ± 0.5278
d) Since the confidence interval obtained in part c does not include the hypothesized value of 82, we can reject the null hypothesis (H_o: μ = 82) at α = 0.010. The hypothesized value of 82 falls outside the confidence interval, providing evidence to suggest that the true population mean is different from 82.
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Write two expressions that are equivalent to 3 . 10^-6
Answer:
636372
Step-by-step explanation:
the answer is 636372
The graph shows the amount of money in a savings account over a period of 10 weeks.
How much money was saved over the 10 week period?
A) $50
B) $80
C) $110
D) $112
Answer:
A) $50
Step-by-step explanation:
Answer:
+$50
Step-by-step explanation:
Day #0 = $30
Day #10 = $80
80 - 30 = 50
:P
Find the relative maximum and minimum values of f(x,y) = x3/3 + 2xy + y2 - 3x + 1. 3
The critical point (1, -1) represents a relative minimum of f(x, y) with a value of -1/3 and (1, -1) is the only extremum or relative maximum of the function.
To find the relative maximum and minimum values of the function f(x, y) = ([tex]x^3[/tex])/3 + 2xy +[tex]y^2[/tex] - 3x + 1, we need to analyze its critical points and classify them using the second partial derivative test.
To find the critical points, we need to compute the partial derivatives of f with respect to x and y and set them equal to zero:
∂f/∂x = [tex]x^2[/tex] + 2y - 3 = 0
∂f/∂y = 2x + 2y = 0
Solving these equations simultaneously, we find x = 1 and y = -1.
Thus, the critical point is (1, -1).
Next, we need to compute the second partial derivatives and evaluate them at the critical point:
∂²f/∂x² = 2
∂²f/∂y² = 2
∂²f/∂x∂y = 2
Now, we can use the second partial derivative test to classify the critical point.
The discriminant D = (∂²f/∂x²) × (∂²f/∂y²) - [tex]\left(\frac{{\partial^2 f}}{{\partial x \partial y}}\right)^2[/tex] = (2)(2) - [tex](2)^2[/tex] = 0.
Since D = 0, the test is inconclusive.
To determine the nature of the critical point, we can examine the function near the critical point.
Evaluating f at the critical point (1, -1), we find f(1, -1) = [tex](1^3)[/tex]/3 + 2(1)(-1) + [tex](-1)^2[/tex] - 3(1) + 1 = -1/3.
Hence, the critical point (1, -1) represents a relative minimum of f(x, y) with a value of -1/3.
There are no other critical points to consider, so we can conclude that (1, -1) is the only extremum of the function.
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What is a simpler form of
5n(3n³−n²+8) ?
Four times the sum of a number r and 4 is equal to 20 less than 10 times the number r. What is the value of r ?
Answer:
r = 6
Step-by-step explanation:
According to the question,
4(r + 4) = 10r - 20
4r + 16 = 10r - 20
16 + 20 = 10r - 4r
6r = 36
r = 36 / 6
r = 6
Simplify sin^2(t)/sin^2 (t) + cos^2(t) to an expression involving a single trig function with no fractions.
The final simplified expression is [tex](sin(t))^2[/tex]is the correct answer.
The given expression is [tex]sin^2(t) / sin^2(t) + cos^2(t).[/tex]
Simplify [tex]sin^2(t)/sin^2 (t) + cos^2(t)[/tex] to an expression involving a single trig function with no fractions:
By using the identity[tex]sin^2 (t) + cos^2 (t) = 1[/tex] we can write, [tex]sin^2(t)/sin^2 (t) + cos^2(t) = sin^2(t)/(sin^2(t) + cos^2(t))[/tex]
Now using the identity [tex]csc^2 (t) = 1/sin^2 (t)[/tex] we get, [tex]sin^2(t)/(sin^2(t) + cos^2(t))= 1/csc^2(t) = (sin(t))^2[/tex]
The final simplified expression is [tex](sin(t))^2.[/tex]
Trigonometry is the study of relationships between angles and sides of triangles. It finds applications in a variety of fields like engineering, physics, architecture, etc. Trigonometric ratios, identities, and functions are the main concepts of trigonometry. Trigonometric ratios of an angle are ratios of the lengths of two sides of a triangle containing that angle. They are sine, cosine, tangent, cosecant, secant, and cotangent, which are abbreviated as sin, cos, tan, csc, sec, and cot, respectively. The primary trigonometric identity is [tex]sin^2 (t) + cos^2 (t) = 1.[/tex]
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70 out of 550 questions on a standardized test are math questions. what percent of the test is mathematics?
Answer:
385 are math quetions.
Step-by-step explanation:
70% of 550 is 385.
What does x equal please help
Answer: 5 1/2 (5.5)
Step-by-step explanation:
add 4 2/3 to 5/6
Let w = {C5 %):a,ber } with the standard operations in M2.2- Which of the following statements is true? The 2x2 identity matrix is in W W is not a subspace of M2x2 because it does not contain the zero matrix the above is true W is a subspace of M2x2. the above is true None of the mentioned
The statement "W is a subspace of M2x2" is true because W satisfies the three conditions for being a subspace.
To determine whether W is a subspace of M2x2, we need to verify three conditions:
W is non-empty: Since W is defined as the set of all 2x2 matrices with a fixed entry of 5, it contains at least one matrix (such as [[5, 5], [5, 5]]).
W is closed under addition: For any two matrices A and B in W, their sum A + B will also have the fixed entry of 5 in the corresponding position. Therefore, the sum of any two matrices in W will still be in W.
W is closed under scalar multiplication: For any matrix A in W and any scalar c, the scalar multiple cA will also have the fixed entry of 5 in the corresponding position. Hence, the scalar multiple of any matrix in W will still be in W.
Since W satisfies all three conditions, it is indeed a subspace of M2x2.
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a study is to be conducted to help determine whether a spinner with five sections is fair. how many degrees of freedom are there for a chi-square goodness-of-fit test? three four five six seven
There are four degrees of freedom for the chi-square goodness-of-fit test in this study. So, correct option is B.
For a chi-square goodness-of-fit test in the context of testing the fairness of a spinner with five sections, the number of degrees of freedom can be determined by subtracting 1 from the number of categories being tested.
In this case, since the spinner has five sections, there are five categories. Therefore, the degrees of freedom for the chi-square goodness-of-fit test would be:
Degrees of freedom = Number of categories - 1
= 5 - 1
= 4
Degrees of freedom represent the number of values in the final calculation of the chi-square test statistic that are free to vary. It determines the critical values and the distribution of the test statistic.
In the case of the chi-square goodness-of-fit test, the test compares the observed frequencies in each category with the expected frequencies under the assumption of fairness. By comparing these frequencies, the test determines if there is a significant deviation from the expected distribution, indicating unfairness in the spinner.
So, correct option is B.
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Can someone plz help me
Answer:
28yd^2
Step-by-step explanation:
the answer is 28 yards squared bud :)
Need help ASAP please
Answer:
It takes more 1/9th because they ar smaller than 1/6th. You would need three 1/9ths and two 1/6th in order for it to equal 1/3
HELP ME PLEASEEEEEEEEEEEE
Answer:
Step-by-step explanation:
There is really only one solution which is the third choice. When you are dealing with the equation in the form of y = mx + b, the b stands for the y-intercept. So, your y-intercept equals -1. When you are finding the x-intercept you can just substitute y for 0(the definition of x-intercept is where the graph crosses the x-axis, meaning y needs to be equal to 0) and you get that x equals 1/5.
Please help divide 5 652 to the ratio 2:3:5 I will give brainliesters
thank you in advance
Answer:
105
Step-by-step explanation:
(-20+5)(58-65)
(-15)(-7)
105
(a) Is 2 ⊆ {2, 4, 6}?
(b) Is {3} ∈ {1, 3, 5}?
Answer:
hola
Como te amo hermoso
Step-by-step explanation:
Te conozco a alguien para mi amor todo
6/2(1+2) this time don't go ogle it because it will say 9
Answer:
9
Step-by-step explanation:
I'm not sure, the answer is still 9, 1+2 is 3 so
6/2(3)
and 6/2 simplified is 3
so 3(3) is 9
Answer:
9
Step-by-step explanation:
1. Simplify the parantheses
(1+2) = 3
2. Turn 3 into a fraction
3 = 3/1
3. Multiply the fractions
6 x 3 = 18
2 x 1 2
4. What is 18/2?
18/2 = 9
Hiii, so I REALLY want to rank up, and I just need 5 more Branliests, so if you liked my answer, can you please give me one? Thank you so much, and thanks for the points!!
The following is a table relating a group of 1000 patients’ true breast cancer statuses and their corresponding test results after receiving a mammogram.
Cancer Status
Test Result
Positive
Test Result
Negative
Total
Breast Cancer
223
80
303
No Breast Cancer
13
684
697
Total
236
764
1000
What is the probability of a positive test, given that the patient has breast cancer? (2 points)
What is the formal term used to describe this probability measure? (2 point)
What is the probability of a negative test, given that the patient is breast cancer free? (2 points)
What is the formal term used to describe this probability measure? (2 point)
The probability of a positive test, given breast cancer, is 223/303, while the probability of a negative test, given no breast cancer, is 684/697.
To find the probability of a positive test, given that the patient has breast cancer, we divide the number of true positive cases (223) by the total number of patients with breast cancer (303). This gives us a probability of 223/303.
The formal term used to describe this probability measure is conditional probability or the probability of an event A occurring given that event B has already occurred. In this case, the positive test is event A, and having breast cancer is event B.
Similarly, to find the probability of a negative test, given that the patient is breast cancer-free, we divide the number of true negative cases (684) by the total number of patients without breast cancer (697). This gives us a probability of 684/697.
The formal term used to describe this probability measure is also conditional probability, where the negative test is event A, and not having breast cancer is event B.
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Anthony currently earns $11.75 per hour.
• He will get a $0.25 raise after 6 months.
• He will get a 2.5% raise after an additional 6 months.
After Anthony gets both raises, what will his pay be for 38 hours of work?
O A. $468.92
o B. $467.40
o
C. $465.50
D. $446.50
N
Answer:
You need to add more information that that. It's too confusing when you put it like that.
Step-by-step explanation:
Answer: girl i'm tryna figure this out too
Step-by-step explanation:
evaluate the following expressions. your answer must be an exact angle in radians and in the interval [ 0 , π ] . example: enter pi/6 for π 6 .
The expression to evaluate is arccos([tex]\sqrt(3)[/tex]/2) - arcsin(1/2). The exact angle in radians in the interval [0, π] for this expression is π/6.
To evaluate the given expression, we start by calculating the values inside the trigonometric functions. The square root of 3 divided by 2 is equal to 0.866, and 1 divided by 2 is equal to 0.5. The arccos function gives us the angle whose cosine is equal to the input. In this case, the cosine of the angle we are looking for is[tex]\sqrt(3)[/tex]/2. Using the unit circle, we find that this angle is π/6 radians. Next, we calculate the arcsin of 1/2, which gives us the angle whose sine is equal to the input. This angle is π/6 radians as well. Finally, we subtract the two angles to get our result: π/6 - π/6 = 0. Therefore, the exact angle in radians in the interval [0, π] for the given expression is π/6.
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2. A bank charges a $10 fee to open an account. Which of the following equations best represents the total amount in the account, m, when starting with d,dollars?
A. m = d + 10
B. m = d -10
C. m –10 = d
D. m + d = 10
PLEASE HELP A.S.A.P
Answer:
B
Step-by-step explanation:
it's b
m= d-10
The equation which best represents the total amount in the account, m, when starting with d dollars is
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
A bank charges a $10 fee to open an account.
Let the account is started with d dollars.
From the amount d, $10 will be taken as an opening fee.
Remaining balance = d - 10
So if m represents the total amount in the account, the,
m = d - 10
Hence the total amount in the account, m, can be represented as m = d - 10, if the account is started with d dollars.
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A store purchases a shirt for $16.89. The store marks up the shirt by 20%. Right now, they are having a sale for 40% off any item. What is the sale price with a 7.25% tax?
Answer:
$13.04
Step-by-step explanation:
First, multiply 16.89 by 1.2, 0.6, and 1.0725. You should get a weird number on your calculator saying 13.042458, but just round 2 to the 4 ( 4 stays the same) and remove all the other numbers to get $13.04
A survey conducted by Sallic Mae and Gallup of 1404 respondents found that 323 students paid for their education by student loans. Find the 90% confidence of the true proportion of students who paid for their education by student loans.
Fifty randomly selected people were asked how long they slept at night. The mean time was 7.1 hours, and the standard deviation was 0.78 hour. Find 95% confidence interval of the mean time. Assume the variable is normally distributed.
For a medical study, a researcher wishes to select people in the middle 60% of the population based on blood pressure. If the mean systolic blood pressure is 120 and the standard deviation is 8, find the upper and lower reading that would qualify people to participate in the study.
The upper and lower readings that would qualify people to participate in the medical study are 113.48 and 126.72 respectively.
Firstly, we'll calculate the 90% confidence interval of the proportion of students who paid for their education by student loans.
For this, we will use the formula:
[tex]$$\hat{p}\pm z\left(\frac{\sqrt{\hat{p}(1-\hat{p})}}{n}\right)$$[/tex]
Where, [tex]$\hat{p}$[/tex] is the sample proportion, n is the sample size, z is the z-score for the level of confidence,
[tex]$1-\alpha$[/tex]
For 90% confidence, the z-score is 1.645 (because the table value of z-score is 1.645 at 90% confidence level).
[tex]\hat{p}=\frac{323}{1404}$$[/tex]
[tex]\hat{p}=0.23$$[/tex]
[tex]\text{Standard Error}= \left(\frac{\sqrt{\hat{p}(1-\hat{p})}}{n}\right)$$[/tex]
[tex]\text{Standard Error}= \left(\frac{\sqrt{0.23(1-0.23)}}{1404}\right)$$[/tex]
[tex]\text{Standard Error}= 0.014$$[/tex]
[tex]\text{Confidence Interval} = \hat{p}\pm z \times \text{Standard Error}$$[/tex]
[tex]\text{Confidence Interval}= 0.23\pm 1.645(0.014)$$[/tex]
[tex]\text{Confidence Interval}= 0.23\pm 0.023$$[/tex]
Confidence Interval = [0.207,0.253]
The 90% confidence interval of the proportion of students who paid for their education by student loans is [0.207,0.253].
Now we will calculate the 95% confidence interval of the mean time.
For this, we will use the formula:
[tex]\bar{X}\pm z\left(\frac{\sigma}{\sqrt{n}}\right)$$[/tex]
Where, [tex]$\bar{X}$[/tex] is sample mean, [tex]$\sigma$[/tex] is population standard deviation, n is sample size, z is the z-score for the level of confidence, [tex]$1-\alpha$[/tex]
For 95% confidence, the z-score is 1.96.
(because the table value of z-score is 1.96 at 95% confidence level).
[tex]\text{Confidence Interval}= \bar{X}\pm z\left(\frac{\sigma}{\sqrt{n}}\right)$$[/tex]
[tex]\text{Confidence Interval}= 7.1\pm 1.96\left(\frac{0.78}{\sqrt{50}}\right)$$[/tex]
[tex]\text{Confidence Interval}= 7.1\pm 0.2199$$[/tex]
Confidence Interval = [6.8801, 7.3199]
The 95% confidence interval of the mean time is [6.8801, 7.3199].
Next, we will find the upper and lower reading that would qualify people to participate in the medical study.
We can do this by calculating the z-scores for the upper and lower percentiles using the standard normal distribution table.
For the lower reading: Since we want to select people in the middle 60% of the population, the lower reading will correspond to the 20th percentile.
Using the standard normal distribution table, we find that the z-score for the 20th percentile is -0.84.
Using the z-score formula, we have:
[tex]z = \frac{x - \mu}{\sigma}$$[/tex]
where, x is the lower reading.
Substituting the given values, we get:-
0.84 = (x - 120) / 8
Solving for x, we get:
[tex]x = (-0.84 \times 8) + 120$$[/tex]
x = 113.48
The lower reading that would qualify people to participate in the medical study is 113.48.
For the upper reading: Since we want to select people in the middle 60% of the population, the upper reading will correspond to the 80th percentile.
Using the standard normal distribution table, we find that the z-score for the 80th percentile is 0.84.
Using the z-score formula, we have:
[tex]z = \frac{x - \mu}{\sigma}$$[/tex]
where, x is the upper reading.
Substituting the given values, we get:
0.84 = (x - 120) / 8
Solving for x, we get:
[tex]x = (0.84 \times 8) + 120$$[/tex]
x = 126.72
The upper reading that would qualify people to participate in the medical study is 126.72.
Therefore, the upper and lower readings that would qualify people to participate in the medical study are 113.48 and 126.72 respectively.
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Rogue River Kayaks specializes in making lightweight yet durable kayaks for white water rafting. It is essential that they make sure that their kayaks maintain a certain level of buoyancy even for the largest of kayakers. According to the latest data set provided by National Transportation and Safety Board (NTSB), the weights of men in the United States are normally distributed with a mean of 188.6 pounds and a standard deviation of 38.9 pounds.
Using excel solve the following:
1. Rogue River Kayaks claims that they can fit 99% of men in their Boulder Buster Kayak. What is the upper weight limit the kayak needs to support for the company to meet their claim? Write or type out the formula you used to calculate your answer.
2. The company claims that the ideal weight range for kayakers in the Boulder Buster is between 135 pounds and 210 pounds. What probability a randomly selected rider falls into this range? Use the characteristics from latest data set as mentioned in the paragraph above to answer this question. Write or type out the formula you used to calculate your answer.
3. Why is it important for Rogue River Kayaks to consistently look to the NTSB to update the distribution of weights in the United States?
1. the upper weight limit the kayak needs to support for the company to meet their claim is 270 pounds (rounded off to nearest pound).
2. the probability that a randomly selected rider falls into the weight range of 135-210 pounds is 0.6245 or approximately 62.45%.
3. It is important for Rogue River Kayaks to consistently look to the National Transportation and Safety Board (NTSB) to update the distribution of weights in the United States because the company needs to ensure that their kayaks can accommodate the maximum number of people possible.
As the distribution of weights in the population changes, the company needs to adjust the design of their kayaks to meet the needs of their customers.
By staying up-to-date with the latest data provided by NTSB, Rogue River Kayaks can ensure that their products remain competitive and continue to meet the needs of their customers.
1. We know that the weights of men in the United States are normally distributed with a mean (μ) of 188.6 pounds and a standard deviation (σ) of 38.9 pounds.
Using Excel, we can use the formula NORM.
INV to find the upper weight limit for the kayak to support if Rogue River Kayaks claims that they can fit 99% of men in their Boulder Buster Kayak.
The formula for NORM.
INV is =NORM.INV(probability,mean,standard deviation)
Where probability = 0.99, mean = 188.6, standard deviation = 38.9.
Thus, =NORM.INV(0.99,188.6,38.9)
= 269.60
Therefore, the upper weight limit the kayak needs to support for the company to meet their claim is 270 pounds (rounded off to the nearest pound).
2. To find the probability that a randomly selected rider falls into the ideal weight range for kayakers in the Boulder Buster, we need to find the z-scores for the given weight range and then use the standard normal distribution table.
The z-score formula is:
z = (x - μ) / σ
where x is the weight, μ is the mean and σ is the standard deviation.
For the lower weight limit of 135 pounds, the z-score is z = (135 - 188.6) / 38.9 = -1.382
For the upper weight limit of 210 pounds, the z-score is z = (210 - 188.6) / 38.9 = 0.551
Using the standard normal distribution table, we can find the probability that a z-score falls between -1.382 and 0.551.
The probability is
P(z < 0.551) - P(z < -1.382)
= 0.7088 - 0.0843
= 0.6245
Therefore, the probability that a randomly selected rider falls into the weight range of 135-210 pounds is 0.6245 or approximately 62.45%.
3. It is important for Rogue River Kayaks to consistently look to the National Transportation and Safety Board (NTSB) to update the distribution of weights in the United States because the company needs to ensure that their kayaks can accommodate the maximum number of people possible.
As the distribution of weights in the population changes, the company needs to adjust the design of their kayaks to meet the needs of their customers.
By staying up-to-date with the latest data provided by NTSB, Rogue River Kayaks can ensure that their products remain competitive and continue to meet the needs of their customers.
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The height of a parallelogram is 4 millimeters more than its base. If the area of the
parallelogram is 221 square millimeters, find its base and height.
Answer:
523 inches
Step-by-step explanation:
got it right on edg
A) Set up an integral for finding the Laplace transform of f(t) = 5.
B) Find the antiderivative (with constant term 0) corresponding to the previous part.
C) Evaluate appropriate limits to compute the Laplace transform of f(t).
D) Where does the Laplace transform you found exist? In other words, what is the domain of f(s)?
a. In this case, since f(t) = 5, L{5} = ∫[0 to ∞] 5 * e^(-st) dt. b. the antiderivative simplifies to ∫(5 * e^(-st)) dt = (5/s) * e^(-st). c. the Laplace transform simplifies to (5/s) * (0 - 1).
A) To set up an integral for finding the Laplace transform of f(t) = 5, we can use the definition of the Laplace transform. The Laplace transform of a function f(t) is given by the integral:
L{f(t)} = ∫[0 to ∞] f(t) * e^(-st) dt
where s is the complex frequency parameter. In this case, since f(t) = 5, we have:
L{5} = ∫[0 to ∞] 5 * e^(-st) dt
B) To find the antiderivative corresponding to the previous part, we can integrate the function 5 * e^(-st) with respect to t. The antiderivative, or indefinite integral, of 5 * e^(-st) dt is:
∫(5 * e^(-st)) dt = (5/s) * e^(-st) + C
where C is the constant of integration. Since we are given that the constant term is 0, the antiderivative simplifies to:
∫(5 * e^(-st)) dt = (5/s) * e^(-st)
C) To evaluate the Laplace transform of f(t) = 5, we need to compute the integral from 0 to ∞. Plugging in the antiderivative from part B, we have:
L{f(t)} = ∫[0 to ∞] 5 * e^(-st) dt = lim[T→∞] [(5/s) * e^(-sT) - (5/s) * e^(-s(0))]
As T approaches infinity, the term e^(-sT) goes to 0, since the exponential function decays as the exponent becomes more negative. Therefore, the Laplace transform simplifies to:
L{5} = lim[T→∞] [(5/s) * e^(-sT) - (5/s) * e^(0)]
= (5/s) * (0 - 1)
Simplifying further, we find:
L{5} = -5/s
D) The Laplace transform L{f(t)} = -5/s exists for values of s where the integral converges. The Laplace transform is defined for a certain range of complex numbers, which forms the domain of the Laplace transform. In this case, the Laplace transform of f(t) = 5 exists for all complex numbers s except for s = 0. Therefore, the domain of f(s) is the set of all complex numbers except for s = 0.
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EASY MATH
Find all the zeros of f(x)= x^3 − 6x^2 + 13x − 20 given that 1−2i is a zero.
x=
Answer:
there is only one zero
Step-by-step explanation: and if it easy why you didint do it just ascking