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 that49.5

%

of them have an IQ score over100

. It is known that50

%

of the general population has an IQ score exceeding100

.Answer the following. (If necessary, consult alist of formulas.)

(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

0.495

, which is the probability that there will be49.5

%

or more individuals with IQ scores over100

in a random sample of400

. Round your answer to four decimal places.