Question

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. A sample of 4 fish is taken. Below what value do 89.62% of the sample mean fall?

A		2.696
B		2.842
C		3.559
D		3.704

Answer 1

Consider, X - Weight of catfish
Given that, X~Normal distribution with
Let - sample mean
Then, will follow normal distribution with

We have to find a such that,
( I have used excel command "=Norminv(probability,mean,stan_dev)" , Here, probability=0.8962,mean=3.2,stan_dev=0.4)

So it gives, a=3.704

So, correct answer is D