4. 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≥p0.53, 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. 5.