Question

The weights of the fish in a certain lake are normally distributed with a mean of 15.9 pounds and a standard deviation of 5.1 pounds. If 5 fish are randomly selected, find the probability that the mean weight is between 11.4 and 18.6 pounds. Round your answer 4 places after the decimal point.

Answer 1

Solution :

Given that ,

mean = = 15.9

standard deviation = = 5.1

n = 5

= 15.9

=  / n= 5.1 / 5=2.2808

P(11.4<    < 18.6) = P[(11.4 -15.9) / 2.2808< ( - ) / < (18.6 -15.9) /2.2808 )]

= P( -1.97< Z < 1.18)

= P(Z <1.18 ) - P(Z <-1.97 )

Using z table

=0.881-0.0244

=0.8566

probability= 0.8566