Question

The weights of the fish in a certain lake are normally distributed with a mean of 9.9 lb and a standard deviation of 2.1. If 75 fish are randomly selected, what is the probability that the mean weight will be between 7.7 and 10.4 lb?

Answer 1

Solution :

Given that ,

mean =   = 9.9

standard deviation = =2.1

n = 75

= 9.9

=  / n= 2.1 / 75=0.2425

P(7.7<     <10.4 ) = P[(7.7-9.9) /0.2425  < ( - ) /   < (10.4-9.9) / 0.2425 )]

= P( -9.72< Z < 2.06)

= P(Z < 2.06) - P(Z <-9.72 )

Using z table

=0.9803-0

0.9803

probability=  0.9803