A recent university survey on the monthly number of hours that students spend commuting states, the average monthly commute time is 20 hours.

Question

If the standard deviation is 7 hours and a random sample of 49 students is selected.
a) What is the probability that the sample average is more than 22 hours?
b) What is the probability that the sample average is less than 21 hours?

I can't seem to figure out what distribution this question is? Would it be normal, binomial, poisson or something else?

Answer 1

You will have to use either tables in your textbook or some kind of software that deals with the Normal Distribution curve.
This is an excellent webpage for this question:
http://davidmlane.com/normal.html

Answer 2

In case your computer breaks down. For normal distribution:

Z = (score-mean)/SE = (22-20)/(7/√49) = ?

SEm = SD/√n

Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportion/probability.