In: Statistics and Probability
The weights of the fish in a certain lake are normally distributed with a mean of14lb and a standard deviation of 9. If 9
fish are randomly selected, what is the probability that the mean weight will be between 11.6 and 17.6lb?
Round your answer to four decimal places.
µ = 14
σ = 9
n= 9
we need to calculate probability for ,
11.6 ≤ X ≤ 17.6
X1 = 11.6 , X2 =
17.6
Z1 = (X1 - µ )/(σ/√n) = ( 11.6
- 14 ) / ( 9 /
√ 9 ) = -0.80
Z2 = (X2 - µ )/(σ/√n) = ( 17.6
- 14 ) / ( 9 /
√ 9 ) = 1.20
P ( 11.6 < X <
17.6 ) = P (
-0.80 < Z < 1.20 )
= P ( Z < 1.20 ) - P ( Z
< -0.80 ) =
0.885 - 0.212 =
0.6731
(answer)