00:01
It's given here that cherry trees in a certain orchard have heights that are normally distributed with the mean of 115 inches and a standard deviation of 14 inches.
00:12
And for part a, we are asked what proportion of trees are more than 128 inches tall? so the proportion is equal to the probability that x is greater than 128.
00:25
And so graphically, if this is our normal distribution for the heights of the cherry trees, it has a mean of 115 in the middle.
00:32
In a standard deviation of 14.
00:36
128 is approximately here.
00:40
And the probability that x is bigger than 128 is equal to the area under the curve to the right of 128.
00:47
So that corresponds to the area of this blue shaded region.
00:52
And because the total area under any density curve is 1, that means the area under the curve to the right of 128 is equal to 1 minus the area under the curve to the left of 128.
01:05
And this means that we can re -express this probability as 1 -1 -128.
01:07
Minus the probability that x is less than or equal to 128.
01:13
And we can use excel to solve this probability.
01:15
So let's go to excel.
01:17
We start a computation with an equal sign.
01:19
We have 1 minus, and we want to use the normal distribution function.
01:23
For the first argument, we enter 128, and then we enter the mean and the standard deviation of the normal distribution.
01:31
For the cumulative argument, we select true because we want the probability that x is less than or equal to 128.
01:38
We hit enter and we get a probability of .1766 approximately...