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...

Extracted 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. |(c) Compute an approximation for P(p 2 0.53), 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.