00:01
We are given here that the emergency service time to respond, we can call that random variable x, is normally distributed with the mean time of 13 minutes and standard deviation of 3 minutes.
00:16
And for part a, we are asked for the probability that for a randomly selected emergency call, the service time is less than 10 minutes.
00:25
So this is the probability that x is less than 10.
00:32
And now if we want to use the standard normal table to solve this, we first must standardize it, and we standardize according to this formula.
00:46
So this is equal to the probability that z is less than 10 minus 13 divided by 3.
01:03
And going to the standard normal table and looking up minus 1, that corresponds to a cumulative probability of 0 .1587.
01:19
And so the probability of response time of less than 10 minutes is .1587.
01:27
And then for part b, we're asked for the probability that the service takes between 12 and 15 minutes.
01:34
So this is the probability that x is between 12 and 15.
01:41
It can be re -expressed as the probability that x is less than 15 minus the probability that x is less than or equal to 12.
01:53
And this time let's use software to solve these.
01:57
And we're going to do it in one step in excel...