A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of

Question

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 52.5% 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 p, where is the proportion of people with IQ scores over 100 in a random sample of 400 people.
(b) Find the standard deviation of p.
(c) Compute an approximation for P(≥0.525), which is the probability that there will be 52.5% or more individuals with IQ scores over 100 in a random sample of 400. Round your answer to four decimal places.

Kunduz · Accepted Answer

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