Q. Numerous studies have been dedicated to investigate the relationship between juvenile delinquency and poor verbal abilities. Suppose that scores of verbal intelligence Quotient (IQ) test have a population mean µ=107 and a population standard deviation 15.

a. What shape would you expect the sampling distribution of x bar for n=84 juveniles to have? Does your answer depend on 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. Situation 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 of verbal IQ of x bar = 110", Considering the answer to part b, do you think that the population mean and standard deviation for nondelinquent juveniles are the same as those of all juveniles. Give an analytical explanation.