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? Write your answer as a decimal rounded to 4 places.

Answer 1

Solution :

Given that,

mean = = 20

standard deviation = = 9

n = 9

= 20

  =  ( /n) = ( 9 / 9 ) = 3

P (17.6 < < 23.6 )

P ( 17.6 - 20 / 3) < ( -  / ) < (23.6 - 20 / 3 )

P ( - 2.4 / 3 < z < 3.6 / 3 )

P (- 0.8 < z < 1.2 )

P ( z < 1.2 ) - P ( z < - 0.8)

Using z table

= 0.8849 - 0.2119

= 0.6730

Probability = 0.6730