Question

In: Statistics and Probability

The weights of the fish in a certain lake are normally distributed with a mean of14lb...

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 17.6​lb?

Round your answer to four decimal places.

Solutions

Expert Solution

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)


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