A machine is shut down for repairs if a random sample of 100 items selected from the daily output of the machine reveals at least 15% defectives. (Assume that the daily output is a large number of items.) Suppose that a random sample of 20 items is selected from the machine. If the machine produces 20% defectives, find the probability that the sample will contain at least three defectives, by using the following methods. (a) the normal approximation to the binomial (Round your answer to four decimal places.)
Answer:
0.7995 = 79.95% probability that the sample will contain at least three defectives.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Suppose that a random sample of 20 items is selected from the machine.
This means that [tex]n = 20[/tex]
The machine produces 20% defectives
This means that [tex]p = 0.2[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 20*0.2 = 4[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.2*0.8} = 1.79[/tex]
Probability that the sample will contain at least three defectives
Using continuity correction, this is [tex]P(X \geq 3 - 0.5) = P(X \geq 2.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 2.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.5 - 4}{1.79}[/tex]
[tex]Z = -0.84[/tex]
[tex]Z = -0.84[/tex] has a pvalue of 0.2005
1 - 0.2005 = 0.7995
0.7995 = 79.95% probability that the sample will contain at least three defectives.
Find the value of x for the right triangle.
45°
х
10
Answer:
14.14
Step-by-step explanation:
sin(45)=10/x. <--fraction
then solve for x you should get this
x=10/sin(45)
and that should equal
14.14213562
5. A flock of geese flies 50 miles per hour. Write a linear
equation that gives the distance d in miles that the flock
of geese flies in h hours
Answer:
y=50x+0
Step-by-step explanation:
y=mx+b is y-intercept form
I will make x= hours and y= distance (miles)
every 1 you add to x has to represent 50 miles
for the y intercept, it was unspecified so I assumed 0
Hope this helps :)
Answer:
y=50x
Step-by-step explanation:
Which step in the proof has a flow?
1.Statement 2
2.Reason 3
3.statement 3
4.Reason 2
Answer:
Reason 2
Step-by-step explanation:
The reason should be transitive property( if a=b and b=c then a=c) not reflective property.
Which rule describes the function whose graph is
shown?
f(x) ={x+6 x<-4
x^2, -2
6- x, x>4
g(x)={x+6, x<-2
x^2, -2
6-x, x>2
h(x)={x+4, x<-2
x^2, -2
4-x, x>2
b. g(x)...
domain: a. (-infinity, infinity)
range: b. (-infinity, 4}
Option (B) is the correct option.
What is the graphing function?"Graphing functions is drawing the curve that represents the function on the coordinate plane. If a curve (graph) represents a function, then every point on the curve satisfies the function equation".
For the given situation,
[tex]f(x) ={x+6 x < -4x^2, -2 6- x, x > 4[/tex]
[tex]g(x)={x+6, x < -2x^2, -2 6-x, x > 2[/tex]
[tex]h(x)={x+4, x < -2x^2, -2 4-x, x > 2[/tex]
Plot the graph for the given functions [tex]f(x), g(x), h(x)[/tex].
After plotting all the functions, the function [tex]g(x)[/tex] describes the graph shown.
Hence, option (B) is the correct option.
Learn more about graphing functions here
https://brainly.com/question/24696306
#SPJ2
I am really confused by this question. Can someone help?
Answer:
192°
Step-by-step explanation:
✔️First, find the value of x:
<G + <T = 180° (opposite angles of an inscribed cyclic quadrilateral are supplementary)
12 + 6x + 5x + 14 = 180 (substitution)
Add like terms
11x + 26 = 180
11x = 180 - 26
11x = 154
x = 154/11
x = 14
✔️m<G = ½(m(FH)) (inscribed angle is ½ of the measure of intercepted arc)
Therefore,
m(FH) = 2(m<G)
m(FH) = 2(12 + 6x) (substitution)
Plug in the value of x
m(FH) = 2(12 + 6*14) = 2(12 + 84) = 192°
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
3rd one
Step-by-step explanation:
Answer:
<VWT and <UTW
<STW and <XWT
Which answer choice represents a person burning 45
calories by climbing 9 flights of stairs?
F
Number of Flights of
Stairs Climbed, f
Number of Calories
Burned, c
G.
c=f+5, where c represents the number of
calories burned and f represents the number of
flights of stairs climbed.
1
5
3
15
5
25
7
35
J
A person who climbs 5 flights of stairs will
burn 1 calorie
90
22
Need
Heln2
please
What is the theoretical probability of the event that a family with two children has two boys? Make a tree diagram to help solve the problem.
a.
One-half
b.
One-fourth
c.
One-sixth
d.
StartFraction 1 Over 8 EndFraction
A vector has initial point of (-1,4) and terminal point (-4,2) write v in component form
Answer:
v = -3i - 2j
Step-by-step explanation:
Vector given two points:
Given two points, a vector is the subtraction of the terminal point by the initial point.
In this question:
Initial point: (-1, 4)
Terminal point: (-4, 2)
So
v = (-4,2) - (-1, 4) = (-4 - (-1), 2 - 4) = (-3,-2)
The vector is v = (-3,-2)
In component form:
xvalue is i, yvalue j. So
v = -3i - 2j
Need help!!!!!!!!!!!
Answer:
90°
-Sum of angles in a triangle= 180°
-angle C is 90°
-therefore angle A + angle B is,
180° - 90° = 90°
Find the diagonal of the rectangular solid with the given measures.
l= 3, w= 3, h= 2
Alan Bissell, market analyst for City Sound Mart, is analyzing the relation between heavy metal CD sales and the size of the teenage population. He gathers data from six sales districts. Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variable is teenage population (in 1,000's). Regression analysis of the data yielded the following tables. For a sales district with 20,000 teenagers, Alan's model predicts annual CD sales of ________________.
Answer:
0.105195x - 0.14156
Step-by-step explanation:
The relationship between heavy metal CD sales and size of teenage population is to be obtained. The attached table shows the result obtained from a regression analysis.
The dependent variable, which is the predicted value or variable, y = heavy metal yield
The Independent variable, predictor variable, x = heavy metal yield
Feommthe table ;
Coefficient of x = slope 0.105195
Intercept = - 0.14156
The general form of a simple linear regression model is :
y = mx + c
c = intercept ; m = slope
Therefore, we have the model :
y = 0.105195x - 0.14156
hey! how's your Saturday going :)
(if it's Saturday for you)
Answer:
great :) wbu
Step-by-step explanation:
Answer:
SMI SABADO VA MUY BIEN DAME CORONA PLISSSSSSSSSSSSS
Step-by-step explanation:
Write an expression for "two multiplied by t".
Please help!!
10 POINTS
Answer:
2*t
Step-by-step explanation:
That should be it...
Just multiply 2 by t
Answer:
2t
"t" is the variable, and is similar to something that would look like this: 2(2)
i think you're overthinking this but I'll help out if I'm wrong
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
<EFC and <DCF
Step-by-step explanation:
Alternate interior angles: Angles that are inside the parallel lines and are opposite from each other
<DCA and <DCF are supplementary angles meaning they add up to 180 degrees.
<EFH and <GFC are vertical angles and both angles are not inside the parallel lines.
<BCF and <GFH are not alternate interior angles because both the angles aren't inside the parallel lines.
<EFC and <DCF are alternate interior angles because they are on opposite sides of the transversal and inside the parallel lines.
What?
AAeEeEeEeOOoooO
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Eeb
What is the volume of a rectangular prism with the demensions: base 7 /2 cm, height 3 /2 cm, and length 9 /2 cm
Answer:
189/8 cm^3
Step-by-step explanation:
Given data
Base= 7/2 cm
Hieght= 3/2cm
Length= 9/2cm
We know that the expression for volume is
Volume = L*B*H
substitute our data
Volume= 7/2*3/2*9/2
Volume= 189/8 cm^3
Hence the volume is 189/8 cm^3
What is the base of a rectangle with a height of 12.6 meters and an area of 28.98 square meters? Enter your answer in the box.
Answer:
why is brainlys ask a tutor not free anymore I really needed help so I pressed the button and all it said was pay for tutor plus
Answer:182.524
Step-by-step explanation:28.98•12.6=365.148 365.148 divided by 2=182.524
Sabrina read 45% of the book that her English teacher
assigned. Which of the following correctly shows 45% as a
decimal and as a fraction?
A. 45%=45/100=9/20 B. 45% = 4.5 = 45/10 = 9/2 C. 45% = 45 = 450/100 = 9/2 D. 45% = 0.045 = 45/1,000 = 9/200
Answer:
A. 45%=45/100=9/20
Step-by-step explanation:
45% is 45 out of 100 or 45/100
9 divided by 20 equals 0.45
They are both equal to 45%
Please look at the picture because I can’t use the keyboard to explain
solve the given inequalitiesa) 2x +3> 15
Answer:
( 3 , 9 )
Step-by-step explanation:
First, add
3
to each segment of the system of inequalities to isolate the
x term while keeping the system balanced:
3 + 3 < 2 x − 3 + 3 < 15 + 3 6 2 x − 0 < 18 6 < 2 x < 18
, divide each segment by 2
to solve for x
while keeping the system balanced:
6 2 < 2 x 2 < 18 2 3 < 2 x 2 < 9 3 < x < 9 Or x > 3 ; x< 9
Brainliest?
TELL WHICH NUMBER IS GREATER.
-7, -16
1)16
2)-16
3)-7
4)7
Solve -4x+6(x+2)=20
A x=9
B x=4
C x=3
D x= -4
Answer:
Step-by-step explanation:
Hello !
-4x+6(x+2)=20
-4x+6x +12 =20
-4x+6x= 20-12
2x = 8
x= 8/2 = 4 => B
A chemist is using 342 milliliters of a solution of acid and water. If 17.7% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
Answer:
60.5 mL
Step-by-step explanation:
Since 17.7% of the solution is acid, and we have 342 mL in total, we just multiply 342 x 0.177 to get 60.5 mL of acid.
I hope this is correct, Best of luck!
A water hose had filled up 1/9 of a pool after
1/4 of an hour. At this rate, how many hours would it take to fill the pool?
Answer:
x=2.25hrs
Step-by-step explanation:
1/9 =1/4hr
9/9=x
(9/9)/(1/9)=1/4.xhr
1/9=1/4.xhr
cross multiplying
4x=9
x=9/4
x=2.25hrs
can you make a triangle with 9 in , 4 in , and 6 in
Answer:
Yes, you can make a triangle with it
Step-by-step explanation:
Given
[tex]Lengths: 9in, 4in, 6in[/tex]
Required
Do the lengths form a valid triangle
To do this, we make use of triangle inequality theorem which states that;
For sides a, b and c;
[tex]a + b > c[/tex]
[tex]b + c >a[/tex]
[tex]a + c > b[/tex]
So, we have:
[tex]9 + 4 > 6[/tex] -- true
[tex]4 + 6 > 9[/tex] -- true
[tex]6 + 9 > 4[/tex] -- true
Since all the inequalities are true, then the sides form a valid triangle
To compare the driving distances for the two models, you arranged an experiment in conjunction with the Par research team. Forty golf balls of each type were subjected to driving-distance tests. You offered the idea of testing the driving distance with a mechanical hitting machine to isolate any mean differences in the distances to the two model golf balls themselves. The results of the tests, with distances measured to the nearest yard, follow.
Let
μ1=population mean driving distance for the current golf ball
μ2=population mean driving distance for the new golf ball
You begin your report to the Par, Inc. management team by offering the following hypothesis pair as a way of representing the problem.
H0 : μ1 - μ2 ≤ 0
H1 : μ1 - μ2 > 0
How would you explain these hypotheses to the management team?
a. We assume that the current model ball has an average driving distance that is greater than the new cut-resistant ball. However, if the new model has a mean driving distance that is greater than or equal to the current model, then we should reject our assumption.
b. We assume that the driving distances for the current model and the new model are equal. If the driving distances between the current and new models are very far apart, then we should reject our assumption.
c. We assume that the current golf ball has an average driving distance that is greater than or equal to that of the new model ball. However, if the new model has a mean driving distance that is significantly longer, then we should reject our assumption.
d. We assume that the new golf ball has an average driving distance that is greater than or equal to that of the current ball. However, if the current model has a mean driving distance that is significantly longer, then we should reject our assumption.
Answer:
d. We assume that the new golf ball has an average driving distance that is greater than or equal to that of the current ball. However, if the current model has a mean driving distance that is significantly longer, then we should reject our assumption.
Step-by-step explanation:
Given that :
μ1=population mean driving distance for the current golf ball
μ2=population mean driving distance for the new golf ball
H0 : μ1 - μ2 ≤ 0
H1 : μ1 - μ2 > 0
The Null hypothesis assumes that the average driving distance of the current golf ball is less than or equal to the average driving distance of the current golf ball
For the Alternative ; If there is significant evidence that the average driving distance of the current golf ball is greater or longer than the average driving distance of the new golf ball ;then we reject our initial claim (the Null hypothesis).
Maria works for an international marketing consulting group. She is studying the monthly demands for Range Rover (suv) in two different cities of the country. She has 180,000 new Range Rovers to ship to the two cities, and she decides to ship 40,000 more to New York City than to Boston. Find the number of (suv) to be shipped to New York City . Please no link I can't open them
Answer:
110,000 (suv) to be shipped to New York City
Step-by-step explanation:
We know that there are 180,000 (suv) to be shipped in total. We also know that there are two cities which these (suv) must be shipped to. So, that is 180,000 (suv) to be shipped to two cities. Let's right a true equation with this information:
Let n represent the number of (suv) to be shipped to New York City and b represent the number of (suv) to be shipped to Boston.
n + b = 180,000
Now, we also know that the number of (suv) to be shipped to New York City is 40,000 greater than the number of (suv) to be shipped to Boston. So, we can write another true equation (for the sake of convenience, let's write it in terms of b rather than in terms of n):
b = n - 40,000
Now that we have a value for b in terms of n, we can plug this value into b in our first equation:
n + (n - 40,000) = 180,000
From here, we can solve:
n + n - 40,000 = 180,000
2n - 40,000 = 180,000
2n = 220,000
n = 110,000
Thus, we have our final answer.
I would appreciate Brainliest, but no worries.
A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows: Women Men _ Sample mean 12.9 hrs 16.4 hrs Sample SD 4.0 hrs 4.2 hrs Sample size 14 17 This sample data is then used to test the claim that the mean time spent watching television by women is less than the mean time spent watching television by men. Assume that the sample variances are equal, and a .05 significance level is used. What can we conclude from this test
Answer:
there is significant evidence to support that the claim that the mean time women spend watching television less than the mean time spent by men.
Step-by-step explanation:
H0 : μw = μm
H1: μw < μm
The test statistic :
(x1 - x2) / sqrt[(sp²/n1 + sp²/n2)]
df1 = 14 - 1 = 13
df2 = 17 - 1 = 16
Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)
Sp² = ((13*4^2) + (16*4.2^2)) ÷ (13 + 16)
Sp² = 16.90
t = (12.9 - 16.4) ÷ sqrt((16.90/14 + 16.90/17))
t = - 3.5 ÷ 1.4836645
t = - 2.359
Using the Pvalue from Tscore ; at 95% ; df = 29
Pvalue = 0.0126
Pvalue < α
0.0126 < 0.05 ;
Hence, we reject the null and conclude that there is significant evidence to support that the claim that the mean time women spend watching television less than the mean time spent by men.