00:01
In this problem, we are given that there is a population, and the values in this population, let's represent that with the random variable x, this is normally distributed, such that the main of the distribution, this is 236 .4, and the standard deviation of the distribution, that's equal to 33 .5, and we draw a sample whose size is 148 out of this population, and we select a value randomly and we have to first determine the probability that this value that we have chosen, it's greater than 231 .4 and this is less than 238 .9.
00:42
So here we first use this formula and let's get the z score corresponding to these two raw scores.
00:49
So when we put the value of x as 231 .4, along with the other variables, the z score will be 231 .4 minus 236 .4.
00:59
Divided by 33 .5, and this simplifies to minus 0 .15 approximately.
01:07
And similarly corresponding to the data value, 238 .9, we get the z score that is 0 .075.
01:15
And we can now say that the probability that x is more than 231 .4, but less than 238 .9.
01:23
This will be equal to the probability that the z score is more than minus 0 .1 .4, but less than 238 .9, and this is less than 0 .075.
01:32
So we can break this and write it as the probability that the z score is less than 0 .075 minus probability that the z score is less than minus 0 .15...