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A researcher wants to investigate the effects of environmental factors on IQ scores

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A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 50.5%of them have an IQ score over 100 It is known that 50% of the general population has an IQ score exceeding 100


(a)Find the mean of p where p is the proportion of people with IQ scores over 100
 in a random sample of 400 people.


(b)Find the standard deviation of p




(c)Compute an approximation for P(p ≥0.505) which is the probability that there will be 50.5%
or more individuals with IQ scores over 100 in a random sample of 400 Round your answer to four decimal places.