00:02
We're told the fuel consumption is normally distributed with an average of 29 and a standard deviation of 5 is shown here in my picture.
00:12
And we want to figure out the probability the sample mean fuel consumption will be fewer than 28 miles per gallon if different sample sizes are taken.
00:21
So with the sample size of 1, we can keep our standard deviation at 5.
00:26
So we're going to need at 28 a z score for 28, which is going to be 28 minus the mean divided by the standard deviation, which is going to make negative 0 .2.
00:42
And then we're going to reference the standard normal probability table, and we're going to look up a z score of negative 0 .20, which is 0 .47.
00:55
So that tells me the area to the left here is 0 .4207.
01:05
So that's the probability of getting a sample mean fuel consumption fewer than 28 miles per gallon with a sample size of one.
01:17
Now, when we switch to a sample size of four, we're going to have to use the central limit theorem, which says our new standard deviation or the standard deviation of all the possible little samples that could be taken is the population standard deviation divided by the square root of our sample size, which is going to be 2 .5.
01:39
So i'm going to number my bell curve now by 2 .5, and now i'm going to mark where 28 is.
01:59
And now we're going to find a z score for 28.
02:02
So i'm going to do 28 minus 29.
02:05
Divided by our standard deviation of 2 .5 is going to give us a new z score of negative 0 .4...