According to the National Center for Education Statistics, the mean costs (fees, room, and board rates) for a four-year public university in the United States was $15 640 for the 2013–2014 academic year. Assume the costs follow a normal distribution with σ = 2000. If a random sample of 60 costs for four-year public university was taken that year,
a) What is the expected value of the sample mean?
b) What is the standard deviation of X̅?
c) What is the probability that the sample mean is over $17 000?
d) What is the probability that the sample mean is within $1000 of the population mean?