Question

The weights of the fish in a certain lake are normally distributed with a mean of 18 lb and a standard deviation of 18 . If 15 fish are randomly selected, what is the probability that the mean weight will be between 16.6 and 21.6 lb?

Answer 1

0.3991

Explanation:

Given that the weights of the fish in a certain lake are normally distributed with a mean of 18 lb and a standard deviation of 18 .

we know that when a sample is taken mean would be the same but std error would vary

when a sample of size 15 is taken we have

`n=15`

Standard error of sample =
`(\sigma)/(√(n) ) \\=2.065`

the probability that the mean weight will be between 16.6 and 21.6 lb

`=P(16.6<x<21.6)\\=P(-0.30<z<0.77)\\=0.3991`

So we get the required probability as

0.3991