A researcher believes that 48% 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 P (p 0.48), which is the probability that there will be 48% or more people with IQ scores over 100 in the sample. Round your answer to four decimal places.