00:01
In this problem we are given that there is a distribution and that's a normal distribution such that the main value of this distribution, which is represented by mu here, that's 10 and the standard deviation.
00:17
This is given to us as two.
00:20
And we have to determine the range of the values such that 68 % of the observations falls between those two values.
00:29
So people consider the two values to be represented by x1 and x2.
00:34
And let's suppose that the z score corresponding to x2, this is represented by z star, and the z score corresponding to x1, this is minus z star.
00:44
So here we consider x to be the values in the distribution and assuming this to be normally distributed as 68 % of the values are between these two values of x.
00:57
So the probability that x is greater than x1, but less than x2, this will be equal to 68%, which will be 0 .68 in terms of decimal.
01:08
And this implies that the probability that the z score is more than minus z star, but less than z star, even this will be equal to 0 .68...