Question
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,
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.
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