3A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.

a.What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean?

b.Confirm that the Central Limit Theorem condition(s) have been met and the sampling distribution

c.What is the probability that these 64 students will spend a combined total of more than $715.21?

d.What is the probability that these 64 students will spend a combined total between $703.59 and $728.45?

e.If the sample size gets smaller, how does that affect the shape of the sampling distribution of sample means?