6 The weights of fish in a certain lake are normally distrib

6. The weights of fish in a certain lake are normally distributed with a mean of 15 lb and a standard deviation of 6 lbs. If 4 fish are randomly selected, what is the probability that the mean weight will be between 12.6 and 18.6 lb?

Solution

ANS) mean = 15 , s.d = 6...sample size = n =4...D.F = 4-1 =3..
standdard error = 6 / sqrt (4) = 3..

Let, X = mean weight..

so, we have to find,
P [ 12.6 <= X <= 18.6 ] = P [ X < 18.6 ] - P [ X < 12.6 ] = P [ Z < ( 12.6 -15) /3 ] - P [ Z < ( 18.6 - 15) /3 ]
= P [Z <   -0.8 ] - P [ Z < 1.2 ] = 0.8418689 - 0.2410995

= 0.6007694......