Question

1. The on-campus housing costs for a semester at a state university are Normally distributed with
a mean of $1553 and a standard deviation of $329.
(a) What is the distribution of the mean on-campus housing cost for a semester at this university
for a random sample of 50 students?
(b) What is the probability that a randomly selected on-campus student spends more than $1200
per semester?
(c) What is the probability that a random sample of 50 students spends an average of less than
$1500?
(d) What is the probability that a random sample of 50 students spends an average of $1450 to
$1600 per semester?

Answer 1

a. By distribution, do you mean the Standard Error of the mean (SEm)?

SEm = SD/√(n-1)

b. Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to your Z score.

c, d. Use same equation above, except substitute SEm for SD.