Over the past 20 years, the Journal of Abnormal Psychology has published numerous studies on the relationship between juvenile delinquency and poor verbal abilities. Assume that scores on a verbal IQ test have a population mean μ = 107 and a population standard deviation σ = 15.
a. What shape would you expect the sampling distribution of x-bar for n = 84 juveniles to have? Does your answer depend on the shape of the distribution of verbal IQ scores for all juveniles?
b. Assuming that the population mean and standard deviation for juveniles with no record of delinquency are the same as those for all juveniles, approximate the probability that the sample mean verbal IQ for n = 84 juveniles will be 110 or more. State any assumptions you make.
c. In one study cited, the researchers found that a sample of n = 84 juveniles with no record of delinquency had a mean verbal IQ of x-bar = 110. Considering your answer to part b, do you think that the population mean and standard deviation for nondelinquent juveniles are the same as those for all juveniles? Explain.