00:01
In this problem, we are given that the number of crimes in the town.
00:05
Let's represent that with the random variable x.
00:08
This is normally distributed, such that the main of the distribution, this is 150, and the standard division of the distribution, that's equal to 36.
00:18
And we have to first determine the probability that the number of crimes during the next year, that would be less than 130, which is represented by this expression.
00:29
And in the next part, we have to find the value which corresponds to 35 % tie of this distribution.
00:37
So let's represent that with x -dash, and we have to get this.
00:41
So first, let's use this formula and get the z score corresponding to this ros score.
00:46
So when we put the value of x as 130, along with the other variables, we will get the value of the z score as minus 0 .56 approximately.
00:56
And we can now say that the probability that x is less than 130, this will be equal to the probability that the z score is less than minus 0 .56.
01:08
And using the z table, we get this as 0 .2877 approximately...