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

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

(a)Find the mean of P^

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(b)Find the standard deviation of p^

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(c)Compute an approximation for Pp0.48 , 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.