00:01
It's stated in this question that the adult male height is normally distributed with a mean of 69 .1 inches and a standard deviation of 2 .29 inches.
00:11
And we are asked for the probability that a randomly selected adult male is between 65 .5 and 72 .1 inches.
00:18
So that is we want the probability that x is between 65 .5 and 72 .1.
00:30
If this graph represents the normal distribution of adult male heights, we have the mean of 69 .1 inches in the center, and 72 .1 is somewhere around here, 65 .5 is somewhere around here.
00:57
Probability that x is between these two values is equal to the area under the curve and between them.
01:02
So that's the area of this blue shaded region.
01:09
Now this can be solved by first expressing this in terms of cumulative probabilities.
01:13
This is equal to the probability that x is less than 72 .1 minus the probability that x is less than or equal to 65 .5.
01:24
And when we have it expressed in terms of cumulative probabilities, we can use software such as excel to solve this problem...