A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of400 people who grew up as the only child. She finds that50.5%of them have an IQ score over100 It is known that50%of the general population has an IQ score exceeding100

(a)Find the mean ofp wherep is theproportion of people with IQ scores over100

in a random sample of400 people.

(b)Find the standard deviation ofp

(c)Compute an approximation forP(p 0.505) which is the probability that there will be50.5%

or more individuals with IQ scores over100 in a random sample of400 Round your answer to four decimal places.