Question

The income of college students is normally distributed with a mean income per year is $12,000 and a standard deviation of $6,000.
a)If we randomly sample 25 college students, what is the probability that the average income of our sample is less than $4,000?
b)If we randomly sample 9 college students, what is the probability that the average income is between $5000 and $20,000?

Answer 1

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√(n-1)

If only one SD is provided, you can use just that to determine SEdiff.

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