Answer:
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
North Catalina:
Population has mean 130 and standard deviation 8 points. Sample of 3. This means that:
[tex]\mu_{N} = 130, s_{N} = \frac{8}{\sqrt{3}} = 4.6188[/tex]
Chapel Mountain:
Population has mean 120 and standard deviation 10 points. Sample of 3. This means that:
[tex]\mu_{C} = 120, s_{C} = \frac{10}{\sqrt{3}} = 5.7735[/tex]
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
We want that: [tex]N - C > 5[/tex]
Distribution N - C:
The mean is:
[tex]\mu = \mu_N - \mu_C = 130 - 120 = 10[/tex]
The standard deviation is:
[tex]s = \sqrt{s_N^2+s_C^2} = \sqrt{4.6188^2+5.7735^2} = 7.3937[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 10}{7.3937}[/tex]
[tex]Z = -0.68[/tex]
[tex]Z = -0.68[/tex] has a pvalue of 0.2483
1 - 0.2483 = 0.7517
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
Write a equation that can be used to find y, the number of gallons water used for showering for x minuets
Answer:
y = 6x
Step-by-step explanation:
To write an equation, find the unit rate or constant of proportionality (k).
Using a point on the line, (3, 18):
Constant of proportionality, k = y/x = 18/3
k = 6
To write an equation, substitute k = 6 into y = kx.
Thus:
y = 6x
What is the solution to the equation 4x + 2(x − 2) = 4x + x − 12? (1 point)
Question 13 options:
1)
−8
2)
−1
3)
1
4)
8
Answer:
It's -8
Step-by-step explanation:
DISTRIBUTE :
4x + 2( x - 2 ) = 4x + x - 12
4x + 2x - 4 = 4x + x - 12
COMBINE LIKE TERMS :
4x + 2x - 4 = 4x + x - 12
6x - 4 = 4x + x - 12
COMBINE LIKE TERMS :
6x - 4 = 4x + x - 12
6x - 4 = 5x - 12
ADD 4 TO BOTH SIDES :
6x - 4 = 5x - 12
6x - 4 + 4 = 5x - 12 + 4
ADD THE NUMBERS/ SIMPLIFY :
6x = 5x - 8
SUBTRACT 5x FROM BOTH SIDES :
6x = 5x - 8
6x - 5x = 5x - 8 - 5x
SIMPLIFY :
x = -8
3 x 3 x 3 x 3 x 3 x 3 as an exponential notation
Answer:
3^6
Step-by-step explanation:
Answer:
3^6
Count how many threes there are and that's the exponent
Please Help!!! I'll Give Best And Brainliest if it lets me!
Answer:
6
Step-by-step explanation:
this is the answer. have a great day.
Suppose it is known that 23% of students at a certain college participate in a textbook recycling program each semester. Complete parts (a) and (b) below. a. If a random sample of 40 students is selected, do we expect that exactly 23% of the sample participates in the textbook recycling program? Why or why not? Choose the correct answer below. A. We expect that exactly 23% of the sample participates in the textbook recycling program, because that is the percentage of students that participate in the program regardless of sample or population size B. We expect that exactly 23% of the sample participates in the textbook recycling program, because a sample always has the same statistics as the population C. We do not expect that exactly 23% of the sample participates in the textbook recycling program. 23% is a population statistic and you cannot know anything about a sample from the population D. We do not expect that exactly 23% of the sample participates in the textbook recycling program. We do expect that the sample proportion will be close to the population proportion, but it will vary by the sample error from sample to sample b. Suppose we take a sample of 400 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be doser to 23% the proportion from a sample size of 40 or the proportion from a sample size of 400? Explain your reasoning. Choose the correct answer below A. The sample with size 40 will be closer to 23% because a smaller sample size has a smaller standard error B. The sample with size 400 will be closer to 23% because a larger sample size has a smaller standard error. C. The sample with size 400 will be closer to 23% because a larger sample size has more variation, D. The sample with size 40 wil be closer to 23% because a smaller sample size has loss variation
Answer:
D. We do not expect that exactly 23% of the sample participates in the textbook recycling program. We do expect that the sample proportion will be close to the population proportion, but it will vary by the sample error from sample to sample
B. The sample with size 400 will be closer to 23% because a larger sample size has a smaller standard error.
Step-by-step explanation:
The mean of sample can be estimated from the population. However, what we only get is the estimated mean of the sample which isn't the exact figure as that of the population. This slight variation in the mean value of the sample is due to sampling error.
According to the Central limit theorem, increasing the sample size yield a sample mean which continously converges to that of the population mean as the sampling error for such distribution drops lower and lower.
The true statements are:
D. We do not expect that exactly 23% of the sample participates in the textbook recycling program. We do expect that the sample proportion will be close to the population proportion, but it will vary by the sample error from sample to sample B. The sample with size 400 will be closer to 23% because a larger sample size has a smaller standard error.The given parameters are:
[tex]\mathbf{P(Recycling) = 23\%}[/tex]
This means that there is a 23% chance that a student in a college participates in textbook recycling
However, it does not mean that the probability is exactly 23% in a sample of 40 students.
This is so because, there may be error in the sampling of the population.
Hence, the true statement is (d)
According to central limit theorem, as the sample size increases, the sample error reduces.
This mean that the probability will be closer to 23% when the sample size increases to 400
Hence, the true statement is (b)
Read more about probability at:
https://brainly.com/question/11234923
HELP WILL MARK BRAINLIEST IF RIGHT!!!
Answer:
im so sorry bt I dont know this one
Step-by-step explanation:
A marketing research firm believes that more than half of adults drink mostly either regular or diet soda. To test this claim, Gallup took a nationally representative sample of 2027 adults and asked them about their soda consumption. The survey shows that 950 of those surveyed drink mostly either regular or diet soda. The test statistics for the above hypthesis test for the proportion of adults who drink mostly either regular or diet soda is:________. (Round your answer to two decimal places)
Answer:
The test statistic is z = -2.82.
Step-by-step explanation:
A marketing research firm believes that more than half of adults drink mostly either regular or diet soda.
This means that the null hypothesis is: [tex]H_{0} = 0.5[/tex]
The alternate hypothesis is: [tex]H_{a} > 0.5[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.5 tested at the null hypothesis:
This means that:
[tex]\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5[/tex]
Gallup took a nationally representative sample of 2027 adults and asked them about their soda consumption. The survey shows that 950 of those surveyed drink mostly either regular or diet soda.
This means that [tex]n = 2027, X = \frac{950}{2027} = 0.4687[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.4687 - 0.5}{\frac{0.5}{\sqrt{2027}}}[/tex]
[tex]z = -2.82[/tex]
The test statistic is z = -2.82.
Use the data on the dot plot to answer the question.
Answer:
5
Step-by-step explanation:
x < 7
Which means 6 and below
only 5 people slept for less than 7 hours
Answer:
5 people
Step-by-step explanation:
Cuz you have to look what’s to the left of 7 and count the dots in 5 and 6
Find the area of the polygon.
The sum of seven and x
Answer:
Step-by-step explanation:
s=7+x
PLEASE HELP 20 POINTS
1 Which parallelograms have congruent diagonals?
only squares
squares and rectangles
squares and rhombuses
squares, rectangles, and rhombuses
2. Which parallelograns have perpendicular diagonals?
only squares
squares and rectangles
squares and rhombuses
squares, recangles, and rhombuses
Answer:
1) squares and rectangles
2) squares and rhombuses
do anybody know how to help me cause i really need it right now.
Answer:
C
Step-by-step explanation:
Answer:
Step-by-step explanation:
The surface area is made up of four triangles and a square base, so the area is four times the area of the triangle plus the area of the base.
A=4(5)(6)/2+5(5)
A=60+25
A=85
This one is the one I need help with my final question
Answer:
vertex C could be at (6,0) or (2,8)
(I'm sorry if I'm wrong, but if not I hope this helps!)
Step-by-step explanation:
vertex C needs to be placed somewhere on the graph where it would form a right angle (and therefore a right-angled triangle as well). vertex C could be at (6,0) or (2,8). this is because at these two points vertex C will form a right angle, therefore making it a right-angled triangle.
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If I had to find the perimeter of triangle, I would:
Group of answer choices
take the square root of the hypotenuse
multiply all sides together
Add all three side measures together
apply the formula for circumference
Answer:
Add all three side measures together
Step-by-step explanation:
That is how you find the perimeter of most shapes.
Hope this helps! :)
Answer:
add all three aide measures together. I'm not sure but I'd someone give another answer go with it. have a nice day
15a > 75. Substitute 5 for a. PLEASE HELP
Answer:
its equal
Step-by-step explanation:
15 times 5 (a) is 75 soooo 75 is equal to 75 maybe
I need help with this due today
Answer: P-22 A-30
P=28 A-28
P=12 A=9
P=18 A=18
Step-by-step explanation:
1. Side lengths are 5,6,5,6- perimeter is 22 Area is 5*6= 30
2. Side lengths are 10,4,4,2,6,2- perimeter is 28 Area can be found by finding the area of the whole region (4*10) and subtracting the missing piece (2*6) so 40-12=28
3. sides are all 3- perimeter is 3*4= 12 and area is 3*3=9
4. sides are 6,3,6,3- perimeter is 18 and area is 3*6=18
For 120 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degrees Fahrenheit. what would be the center line
Answer:
46° Fahrenheit
Step-by-step explanation:
Center line can be said to be the X double bar. X double bar is the average value we have across all components we're considering. In this question, the X double bar is already given as 960 bottles (if you multiply 120 days by 8 bottles per day) and that it is 46 degrees Fahrenheit.
As such, there exist no reason to want to or have to solve for anything since it's already given.
Therefore the Centre line is 46 degrees Fahrenheit, same as what is given in the question.
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Solve for w. 7(-2w + 3) = 1 - 4w
what is the value of w?
Answer:
w=2
Step-by-step explanation:
-14w + 21 = 1 - 4w
-10w + 21 = 1
-10w = -20
w = -20/-10
w=2
Answer:
20 - 10 W = 0
-7 (2w - 3) = 1 - 4w
21 - 14w = 1 - 4 w
w = 2
HOPE THIS HELPS <3 :) HAVE A NICE DAY
Steve watched television for 3/4 hour on Monday and 5/6 hour on Tuesday. How much longer did he watch television on Tuesday than on Monday?
_______ hour
What is the solution of the equation 4 1/5 + x = 4 3/5
[tex]4 \frac{1}{5} + x = 4 \frac{3}{5} \\ \\ x = 4 \frac{3}{5} - 4 \frac{1}{2} \\ \\ x = \frac{2}{5} [/tex]
a = 3 and c = 12 c/a =
Answer:
4, because 12/3 is 4 cause 3×4=12
Answer: 4
Step-by-step explanation: you need to divide 12 and 3 to get 4.
May someone pls help me with this question
Answer:
Step-by-step explanation:
P(BorL)=(2/8)+(1/8)=(3/8)
He is expected to wear boots or loafers in the next 264 days
264(3/8)=99 of those days
A rocket is launched from a tower. The height of the rocket, y in feet, is rel
time after launch, x in seconds, by the given equation. Using this equation
time that the rocket will hit the ground, to the nearest 100th of second.
y = -16x² + 147x + 80
9514 1404 393
Answer:
9.70 seconds
Step-by-step explanation:
The zero of the equation can be found using the quadratic formula.
ax² +bx +c = 0
x = (-b ±√(b² -4ac))/(2a)
We are only interested in the positive value of x, so this will be ...
x = (-147 -√(147² -4(-16)(80)))/(2(-16)) = (147 +√2679)/32
x ≈ 9.7028 ≈ 9.70 . . . . seconds
The rocket will hit the ground after about 9.70 seconds.
A veterinarian sampled 235 sheep from a large herd to obtain a 90% confidence interval for the mean weight of wool from the sheep. The interval was (23.7 lbs., 33.6 lbs.). If the veterinarian had used a 95% confidence interval instead, the confidence interval would be:_____.A. Wider and would have a smaller chance of missing the true mean. B. Narrower and would have a larger chance of missing the true mean. C. Narrower and would have a smaller chance of missing the true mean. D. Wider and would have a larger chance of missing the true mean. E. Wider but the chance of missing the true mean cannot be determined.
Answer:
A. Wider and would have a smaller chance of missing the true mean.
Step-by-step explanation:
Margin of error for a confidence interval:
The margin of error for a confidence interval is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level(the higher the confidence level, the higher the value of z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
95% confidence interval
Would be wider than the 90% confidence interval, due to the higher value of z.
Also, a x% confidence interval has a x% chance of having the true mean, and a (100-x)% probability of missing the true mean.
Then, a 95% confidence interval has a smaller(5%) chance of missing the true mean compared to the 90% confidence interval(10%). This means that the correct answer is given by option A.
Explain how to solve the equation.
Answer:
or Subtract the same value from both sides.
Clear out any fractions by Multiplying every term by the bottom parts.
Divide every term by the same nonzero value.
Combine Like Terms.
Factoring.
Expanding (the opposite of factoring) may also help.
Recognizing a pattern, such as the difference of squares.
More items...
https://www.mathsisfun.com › algebra
Solving Equations - Math is Fun
Which three steps are correct when solving this quadratic equation by completing the square? X^2-10x=39
Step-by-step explanation:
Any answer that involes,
Step 1: Complete the Square
[tex] {x}^{2} - 10x = 39[/tex]
[tex]( \frac{ - 10}{2} ) {}^{2} = 25[/tex]
[tex] {x}^{2} - 10x + 25 = 64[/tex]
Step 2: Turn the left side into a binomial
[tex](x - 5) {}^{2} = 64[/tex]
Step 3: Solve for x.
[tex]x - 5 = + - 8[/tex]
[tex]x - 5 = 8[/tex]
[tex]x = 13[/tex]
OR
[tex]x - 5 = - 8[/tex]
[tex]x = - 3[/tex]
X=-3 or X=13
Help please plzzzzzzzz
Answer:
60
Step-by-step explanation:
120 + 90 + 90 + 60 = 360
ooooooof i need some help; please explain
Answer:
just say i did it and that it got undone
Step-by-step explanation:
Explain why (x+1)(3x-6) is NOT a complete factorization of 3x^2-3x-6
Answer:
The real answer is:
3x^2 -6x+3x-6
Step-by-step explanation: