The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the probability that the mean weight will be between 9.6 and 15.6 lb? Round your answer to four decimal places.

The probability that the mean weight will be between 9.6 and 15.6 lb is 0.6731

Step-by-step explanation:

Here we have

P(9.6≤≤15.6)

Therefore, we have

Where:

= Sample mean

μ = Population mean = 12

σ = Population standard deviation = 6

n = Sample size = 4

When = 9.6 we have

= -0.8

From Z table, that is 0.21186

When = 15.6 we have 1.2

= 1.2

From Z table, that is 0.88493

0.88493 - 0.21186 = 0.67307

P(9.6≤≤15.6) = 0.67307 which is 0.6731 to four decimal places.