The lengths of fullgrown male stoats are known to be normall

The lengths of full-grown male stoats are known to be normally distributed with a mean of 10.1 inches and a standard deviation of 0.9 inches. What is the probability that a randomly selected stoat will:

a) be at least 10 inches long?

b) be less than 8 inches or more than 12 inches long?

Solution

mean = u = 10.1
SD = 0.9

a) be at least 10 inches long?

z = (x - U) / SD
z = (10 - 10.1) / 0.9
z = -1/9

So, from the link :
https://www.easycalculation.com/statistics/p-value-for-z-score.php
and looking at the z > 1, we get 0.5442

So, the required probability is 0.5442 ---> ANSWER

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b) be less than 8 inches or more than 12 inches long?

First we can find more than 8 and then less than 12
And then subtract those results...

z = (x - U)/SD
z = (8 - 10.1)/0.9
z = -7/3
And use the same link and look at the value z > 1, we get
0.9902

z = (x - U)/SD
z = (12 - 10.1)/0.9
z = 2.1111111111111111111111111111111111111111111111111111
And same link but z < 1, we get
0.0174

So, required probability for between 8 and 12 is :
0.9902 - 0.0174
0.9728 ---> ANSWER