Question

The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 lb?

Answer 1

= 20

= 9

n = 9

SE = /

= 9/ = 3

To find P(17.6 < <23.6):

Case1: For from 17.6 to mid value:
Z = (17.6 - 20)/3 = - 0.80

Table of Area Under Standard Normal Curve gives area = 0.2881

Case2: For from mid value to 23.6:
Z = (23.6 - 20)/3 = 1.20

Table of Area Under Standard Normal Curve gives area = 0.3849

So,

P(17.6 < < 23.6) = 0.2881 + 0.3849 = 0.6730

So,

Answer is:

0.6730