A researcher believes that 51% of people who grew up as the only child have an IQ score over

100. However, unknown to the researcher, this figure is actually 50% , which is the same as in the general population.

To attempt to find evidence for the claim, the researcher is going to take a random sample of 400 people who grew up as the only child. Let p be the proportion of people in the sample with an IQ score above 100.

(a)Find the mean of p

(b)Find the standard deviation of p.

c)Compute an approximation for Pp0.51, which is the probability that there will be 51%or more people with IQ scores over

100 in the sample. Round your answer to four decimal places.