00:01
The average teacher's salary in connecticut is $57 ,337.
00:08
Suppose the distribution is normal and has a standard deviation of $7 ,500.
00:14
Part a, what is the probability that a randomly selected teacher makes less than $52 ,000, excuse me, per year? so we'll do z is less than $52 ,000 minus $57 ,337 ,000 divided by $7 ,500.
00:32
That's going to give us a z value of negative .71, which corresponds to .2389.
00:40
For part b, if we sample 100 teachers, what's the probability that their mean is less than 56 ,000? so this is going to change our standard deviation.
00:53
It will have 7 ,500 divided by the square root of 100, which would be 750.
00:58
So we'll take the probability that z is less than 5 ,000, or excuse me, 56 ,000 minus 57 ,337 divided by 750.
01:09
So that gives us a z value of negative 1 .78 for a probability of 0 .0375.
01:17
So pretty low probability that the sample mean of 100 teacher salaries would fall below...