00:01
So in this sample we're told that heights of people of the same sex are on similar ages are close to normal.
00:08
It says we know that from government data standard deviation of heights of young men is about 2 .8 inches.
00:14
It says suppose that we know the mean height of all male students at this certain college campus is 70 inches.
00:20
So let's jot that down.
00:21
Our mean here is 70 and our standard deviation is 2 .8 and that's for the population.
00:28
Part a says that if we choose one student at random what's the probability he will be between 69 and 71 inches tall.
00:36
What we're finding here is the probability of x being between 69 and 71.
00:41
First thing we need to do is find z -scores for both of these numbers using the red z equation i have on the screen.
00:48
Starting with 69 and using that equation z is equal to x which is 69 minus the mean which is 70 divided by standard deviation which is 2 .8.
00:59
Now if we type that into our calculator and round to two decimal places we come out with our z -score which is negative 0 .36.
01:08
Let's now do the same for 71.
01:11
Z is equal to x which is 71 minus the mean divided by the standard deviation.
01:18
Again calculate that and we'll put this can come out with positive 0 .36 as our z -score.
01:24
Now that we have those two z -scores let's turn to our z -table over here on the left side of the screen and find them.
01:30
So negative 0 .36 gives us 0 .3594.
01:38
Positive 0 .36 gives us 0 .6406.
01:45
To find the area between these two values we'll have to subtract our lesser value from our greater one taking 0 .6406 minus 0 .3594 and that comes out to 0 .2812 or 28 .12 percent chance...