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 53% 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 p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people. (b) Find the standard deviation of p.

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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 53% 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 p, where p is the proportion of
people with IQ scores over 100 in a random
sample of 400 people.
(b) Find the standard deviation of p.
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 53% 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 p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people. (b) Find the standard deviation of p.
sample of 400 people.
(b) Find the standard deviation of p.
00
(c) Compute an approximation for P20.53), which is
the probability that there will be 53% or more
individuals with IQ scores over 100 in a random
sample of 400. Round your answer to four
decimal places.
Transcribed Image Text:sample of 400 people. (b) Find the standard deviation of p. 00 (c) Compute an approximation for P20.53), which is the probability that there will be 53% or more individuals with IQ scores over 100 in a random sample of 400. Round your answer to four decimal places.
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