13. The shoe sizes for NBA players are normally distributed with a mean of 15.4 and a standard deviation of 1.7. Use this information answer the following questions.

a. Have the requirements for the Central Limit Theorem been met? Explain completely.

b. Suppose that we wanted to create a sampling distribution for the mean shoe size for samples of size n=42, would the sampling distribution be approximately normal? What would the mean and standard deviation of the sampling distribution be? Showall work and explain how you know in complete sentences

c.    What is the probability that an individual NBA player would have a shoe size greater than size 14? Find thez-score, Write the appropriate notation and construct a graph.

d.    What is the probability that a sample of size42 would have a mean between 15.5 and 17.5? Find the z-scores for15.5 and 17.5.  Write the appropriate notation and construct agraph.

e. What is the 40th percentile for the mean shoesize for samples of size n=42? Draw the graph and give the shoesize.