What are the answers to these questions?

Question

The mean college loan debt for graduating students is $37,172 with a standard deviation of $2,056. If all possible random samples of size 144 are taken from this population, determine the following:

a) the name of the Sampling Distribution

b) the mean and standard error of the sampling distribution

of the mean (use the correct name and symbol for each)

c) percent of sample means that are greater than $37,392

d) probability that sample means fall within one standard deviation of the mean.

e) Below which sample mean can we expect to find the lowest 25% of all the sample means?

Answer 1

a) sampling distribution of the means

b) mean is the population mean; standard error is the population standard deviation/square root (sample size)

c) z-stat = (37392 - 37172)/(2056//qrt(144))

determine P(z > z-stat)

d) 68%

e) 25th percentile z = -0.67

-0.67 = (x - 37172)/(2056/sqrt(144))

solve for x