00:02
To figure out these different probabilities, we're going to be applying the central limit theorem, which says if we repeatedly took samples of 36 customers and calculated their average time at the tellers window, those averages are going to form a bell curve centered at the population mean of 2 .7, and the standard deviation of all those little samples is going to be found by taking the population standard deviation, 1 .2, and dividing it by the square root of our sample size.
00:31
And that's going to give us a standard deviation of 0 .2.
00:37
And now i'm going to number my bell curve to the right and to the left by 0 .2.
00:45
And now we're ready to answer our questions.
00:49
At most, 2 .4 minutes.
00:52
So 2 .4 minutes would fall right here at negative 1 .5 standard deviations below the mean.
01:01
So the z score is negative 1 .5.
01:04
So we're going to turn to the standard normal probability table and look up a z score of negative 1 .50.
01:11
And that tells us this area, which is going to be our probability, is 0 .0668.
01:22
So that's the answer for part a.
01:27
0668.
01:28
Now for part b, we're looking for more than 3 .1 minutes.
01:33
So notice 3 .1 is exactly two standard deviations above the means, so the z score here is positive 2...