The population of all Harvard students spends an average of $330 per semester on books. The...

The population of all Harvard students spends an average of $330 per semester on books. The population standard deviation of this expenditure is $65. A simple random sample of 40 students who attend the college is taken.

a. Provide the sampling distribution for the sample mean. Can you assume a normal distribution for the sample mean? Why or why not?

b. Calculate the probability that the average expenditure for the 40 students in the sample is between $320 and $350.

c. Calculate the probability that the average expenditure for the 40 students in the sample is less than $300.

d. If we increase the sample size to 50, show and explain what happens to the standard error. Without showing calculations, how would this change in sample size affect the probabilities you calculated in both b and c? Be specific.

Expert Solution

orchestra answered 1 year ago

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