00:02
For this question, we were told that the police response time for an emergency call has a normal distribution with a mean of 8 .4 minutes and a standard deviation of 1 .7 minutes.
00:14
And we were asked for a randomly selected call.
00:17
In part a, what is the probability that the response time is between 5 and 10 minutes? so this is the probability that x is between 5 and 10.
00:28
If this graph represents the normal distribution of response times, the mean of 8 .4 is in the center.
00:36
10 minutes would be approximately here, and 5 minutes here.
00:48
And so the probability that x is between these two values is equal to the area under the curve and between them.
00:55
So that corresponds to the area of this balus shaded region.
01:01
Now to solve this, we first express it in terms of cumulative probabilities.
01:04
This is equal to the probability that x is less than 10, minus the probability that x is at most 5.
01:14
Let's use software to solve this problem.
01:16
So if we use excel, we start a computation with an equal sign.
01:22
We have two terms.
01:23
Both terms use the normal distribution function.
01:26
So for the first term, we find the normal distribution function highlighted here in blue.
01:29
Select that.
01:31
Enter 10 for the first argument, and then the mean, then the standard deviation.
01:37
And for the cumulative argument we enter true to get the probability that x is anything less than 10...