MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 51.5% of them have an IQ score over 100. It is known that 50% of the general population has an IQ score exceeding 100.
Answer the following. (If necessary, consult a list of formulas.)
(a) Find the mean of \(\hat{p}\), where \(\hat{p}\) is the proportion of people with IQ scores over 100 in a random sample of 400 people.
[Box for answer]
(b) Find the standard deviation of \(\hat{p}\).
[Box for answer]
(c) Compute an approximation for \(P(\hat{p} \geq 0.515)\), which is the probability that there will be 51.5% or more individuals with IQ scores over 100 in a random sample of 400. Round your answer to four decimal places.
[Box for answer]](https://content.bartleby.com/qna-images/question/915c192e-d8ba-4859-b60e-5e514228af12/c6e17872-0d46-4ad6-b54c-d9e8ffe5da1f/yb0oe3r_processed.jpeg)
Transcribed Image Text:A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 51.5% of them have an IQ score over 100. It is known that 50% of the general population has an IQ score exceeding 100.
Answer the following. (If necessary, consult a list of formulas.)
(a) Find the mean of \(\hat{p}\), where \(\hat{p}\) is the proportion of people with IQ scores over 100 in a random sample of 400 people.
[Box for answer]
(b) Find the standard deviation of \(\hat{p}\).
[Box for answer]
(c) Compute an approximation for \(P(\hat{p} \geq 0.515)\), which is the probability that there will be 51.5% or more individuals with IQ scores over 100 in a random sample of 400. Round your answer to four decimal places.
[Box for answer]
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Solution:
From the given information, n = 400, p-hat = 0.515 and p = 0.50.
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