Question

The weights of the fish in a certain lake are normally distributed with a mean of 15.2 pounds and a standard deviation of 4 pounds. If 6 fish are randomly selected, find the probability that the mean weight is between 13.6 and 17.6 pounds.

Round your answer 4 places after the decimal point.

Answer 1

Solution :

Given that,

mean = = 15.2

standard deviation = = 4

n = 10

= 15.2

₌ / n = 4 6 = 1.6330

P (13.6 < x < 17.6 )

P ( 13.6 - 15.2 /1.6330) < ( - /)< ( 17.6 - 15.2 / 1.6330)

P ( - 1.6 / 1.6330 < z < 2.4 / 1.6330 )

P (-0.98  < z <1.48 )

P ( z < 1.48 ) - P ( z < - 0.98 )

Using z table

= 0.9306 - 0.1635

= 0.7671

Probability = 0.7671