00:01
In this problem, we are given that there is a random variable x, and this is having normal distribution, such that the mean of the distribution, this is equal to 49, and the standard deviation, well, that's equal to 10, and we have to determine the probability that x is greater than 38, and this is less than or equal to 55, and also draw the normal distribution curve representing this area.
00:27
So first, let's use this formula and get the z score corresponding to these two raw scores.
00:33
So when we put the value of x as 38, along with the other variables, we will get the value of the z score as minus 1 .1.
00:42
And similarly corresponding to the data value 55, we get the z score that is 0 .6.
00:48
And we can now say that the probability that x is more than 38, but less than or equal to 55.
00:55
This will be equal to the probability that the z score is more than minus 1 .1, and that's less than or equal to 0 .6.
01:04
So we can break it and write it as the probability that the z score is less than 0 .6, minus probability that the z score is less than minus 1 .1.
01:14
And using the z table, we get these probabilities as 0 .7258 and 0 .1357 respectively.
01:22
So taking the difference, we get 0 .5901 as the result...