In a recent​ poll, 45​% of survey respondents said​ that, if they only had one​ child, they would prefer the child to be a boy. Suppose you conducted a survey of 130 randomly selected students on your campus and find that 72of them would prefer a boy. ​(a) Use the normal approximation to the binomial to approximate the probability​ that, in a random sample of 130 ​students, at least 72would prefer a​ boy, assuming the true percentage is 45​%.​(b) Does this result contradict the​ poll? Explain.

Question
Asked Oct 26, 2019
75 views
In a recent​ poll, 45​% of survey respondents said​ that, if they only had one​ child, they would prefer the child to be a boy. Suppose you conducted a survey of 130 randomly selected students on your campus and find that 72
of them would prefer a boy.
 
​(a) Use the normal approximation to the binomial to approximate the probability​ that, in a random sample of 130 ​students, at least 72
would prefer a​ boy, assuming the true percentage is 45​%.
​(b) Does this result contradict the​ poll? Explain.
check_circle

Expert Answer

Step 1

Given data

p= 0.45

n =130

Checking the validity of normal approximation

130 x 0.45 = 58.5 > 5
np
np(1 p)
130 x 0.45 x 0.55
32.175 5
So, we can apply normal approximation
а)
Probability that, in a random sample of 130 students, at least 72 would prefer a boy is
giveb by
wwwwwe
P(X 72)
Changing into standard Normal variate
72 58.5
)-1
2.379 1 P(Z < 2.379)
=> P Z 2
130 x 0.45 x 0.55
=> 1 - 0.99132 = 0.00868
(P(Z 2.379) = 0.99132From excel = NORM.S.DIST (2.379,TRUE)
help_outline

Image Transcriptionclose

130 x 0.45 = 58.5 > 5 np np(1 p) 130 x 0.45 x 0.55 32.175 5 So, we can apply normal approximation а) Probability that, in a random sample of 130 students, at least 72 would prefer a boy is giveb by wwwwwe P(X 72) Changing into standard Normal variate 72 58.5 )-1 2.379 1 P(Z < 2.379) => P Z 2 130 x 0.45 x 0.55 => 1 - 0.99132 = 0.00868 (P(Z 2.379) = 0.99132From excel = NORM.S.DIST (2.379,TRUE)

fullscreen
Step 2

b)

considering the significance level 0.05

probability = 0.00868 < 0.05...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Grouping individuals into low, middle and high categories implies a scale of which type? Nominal O...

A: Levels of measurement:The variables can be classified based on the values that can be assigned to th...

question_answer

Q: 4.A college student is interested in whether there is a difference between male and female students ...

A: 1.Here the samples are drawn from the normal population and the population standard deviations are u...

question_answer

Q: The population standard deviation (σ) is necessary for conducting a ___________. A One-sample t -tes...

A: A z-test is defined as a statistical procedure that is used to determine whether the sample mean dif...

question_answer

Q: Suppose an individual was studying temperature’s effect on the crime rate. The researcher looked at ...

A: Solution:The sample mean is obtained below:From the given information, number of observations is 6 a...

question_answer

Q: Interested in learning more about its fans, the marketing office of the AFL conducted a survey at on...

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are sol...

question_answer

Q: A sample selected by taking the members of the population that are easiest to reach is called a ____...

A: Convenience samplingA sample that is made up by people that are easy and very convenient to reach is...

question_answer

Q: 2.Researchers studied selenium levels in beef raised in a low selenium region of the United States. ...

A: Note:Hey there! Thank you for the question. According to our policy, we have solved the first 3 part...

question_answer

Q: The College Board National Office recently reported that in 2011-2012, the547,038 high school junior...

A: a) The probability that a high school junior who takes the test will score at least 610 on the mathe...

question_answer

Q: Please show steps for TI 84 as well.

A: Introduction:Suppose a random variable X has mean μ and standard deviation, σ. Then, the z-score cor...