00:01
So to start out with, we're assuming that these times are normally distributed.
00:05
So we can do z -scoring.
00:06
The mean is 130 .9, and the standard deviation is 32.
00:11
To find a z -score, we're going to do x minus the mean divided by the standard deviation.
00:18
And right before the question a, it asks if the variable is quantitative or qualitative.
00:22
So distance is quantitative, if we're looking at distance in miles to the nearest school.
00:30
So the first one asks what's the chance that the probability is going to be less than 87 seconds.
00:35
So i have my z -score formula set up with the 130 .9 over the 32.
00:39
So i'm just going to plug in an 87 right there and calculate the z -score.
00:44
You end up getting a negative 1 .37.
00:49
And so to get the probability, the area under the curve here to the left, you can go to your calculator, your ti -84 or 83, and do second vars.
00:59
The second button is called the normal cdf, and i have an interval there from negative infinity to negative 1 .37.
01:08
Or you can go to a z -table and look up negative 1 .37, and you'll get the same answer either way.
01:13
That first answer is 0 .0853.
01:19
It's going to go to four decimal places.
01:21
So there we go.
01:23
For part b, we're looking at greater than 186 seconds.
01:26
So i'm going to put 186 right there again in that x spot and calculate a z -score.
01:31
This time i'm going to get a z -score of 1 .72.
01:39
And then again, i'm looking at the upper interval this time.
01:42
So when i put that in my calculator, it's going to be 1 .72 comma infinity this time...