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Relationship-Juvenile delinquency and poor verbal abilities

Numerous studies have been dedicated to investigate the relationship between juvenile delinquency and poor verbal abilitiies. Assume that scores of Verbal Intelligence Quotient (IQ) test have a population mean ...
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 of 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 of all juveniles. Provide an analytical explanation.
(Please see attached file).

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(a) n = 84 is greater than 30.  We can expect the sampling distribution for the 84 juveniles to be approximately normally distributed. This is irrespective of the shape of the distribution of verbal IQ scores ...

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The relationship between juvenile delinquency and poor verbal abilities are provided. A Complete, Neat and Step-by-step Solution is provided in the attached file.

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