00:02
We've got a normal distribution centered at 183 and a standard deviation of 20 as i've drawn here in our picture.
00:09
And we want to figure out the probability of randomly selecting a family that spends between 140 and 190 per week on groceries.
00:17
Or in other words, we want the area underneath the bell curve between these two red and green markers.
00:23
So we're first going to need a z score for each one of those markers.
00:27
So we'll start with 145.
00:30
We'll do 145 minus the mean divided by our standard deviation, and that's going to give us as a z score negative 1 .90.
00:46
So now i'm going to turn to the standard normal probability table and look up a z score of negative 1 .90, and this area to the left of that is 0 .087.
00:59
Now we need a z score for 190.
01:02
So we'll do 190 minus 183 divided by 20.
01:10
So that's going to be 7 divided by 20, which is 0 .35.
01:16
Going back to the standard normal probability table, 0 .35, the area to the left of that is 0 .638...