00:01
It's given here that the time needed to complete an exam in a college campus is normally distributed with the mean of 80 minutes and a standard deviation of 10 minutes.
00:12
And for part a, we were asked for the probability of completing the exam in one hour or less.
00:21
So one hour is 60 minutes.
00:24
So we want the probability that x is less than or equal to 60.
00:29
So if this graph represents the normal distribution for the time taken to complete the exam, there's a mean of 80 exactly in the center, and a standard deviation of 10.
00:41
So 60 is around here, and the probability that the time is less than or equal to 60, is equal to the area under the curve, and to the left of 60.
00:56
Now we can use the standard normal table to solve this probability, and we standardize the random variable according to this formula.
01:03
So if we do that, this is equal to the probability that z is less than or equal to minus 2.
01:17
And now we can look up z equals minus 2 in the standard normal table.
01:22
And we can see that that corresponds to a cumulative probability of 0 .028.
01:34
So 0 .028 is the probability of finishing the exam in one hour or less.
01:42
For b, we want the probability that a student will complete the exam in more than 60 minutes and less than 75.
01:51
So this is the probability that x is between 60 and 75, and this can be expressed as the probability that x is less than 75, minus the probability that x is at most 60.
02:11
If we standardize, we have the probability that z is less than minus one -half, minus the probability that z is less than are equated minus 2...