Question

I am working on a review sheet and got everything except for this one. I am not sure whether to use z or t.

The number of hours per week that high school juniors watch TV is normally distributed with a mean of 8 hours and a standard deviation of 2 hours. If 100 students are chosen at random, find the probability that the mean for that sample is between 8.2 and 8.8.
a. 1598 b. .1586 c. .1156 d. .1152

Note: standard deviation/ the square root of n.
Check out the Central Limit Theorem

Answer 1

Use z-scores.

For this problem:
z = (x - mean)/(sd/√n)

With your data:
z = (8.2 - 8)/(2/√100) = 1.00
z = (8.8 - 8)/(2/√100) = 4.00

Answer: .1586 is the probability (check a z-table between z = 1.00 and z = 4.00)

Answer 2

Thanks!! That really helped. I had the steps you had, but was stuck on z vs t.