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 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.   (c)Compute an approximation for P≥p0.515, which is the probability that there will be 51.5% or more individuals with IQ scores over 100 in a random sample of 400.

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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 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.
 
(c)Compute an approximation for P≥p0.515, 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.
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