Question

The bass in Clear Lake have weights that are normally distributed with a mean of 2.2 pounds and a standard deviation of 0.6 pounds. Suppose you catch a stringer of 6 bass with a total weight of 15.9 pounds. Here we determine how unusual this is. (a) What is the mean fish weight of your catch of 6? Round your answer to 1 decimal place.

______ pounds
(b) If 6 bass are randomly selected from Clear Lake, find the probability that the mean weight is greater than the mean of those you caught. Round your answer to 4 decimal places. ________ (c) Which statement best describes your situation?

_____ This is not particularly unusual because the mean weight of your fish is only 0.5 pounds above the population average.

_____ This is unusual because the probability of randomly selecting 6 fish with a mean weight greater than or equal to the mean of your stringer is less than the benchmark probability of 0.05.

Answer 1

Explanation:

(a) What is the mean fish weight of your catch of 6? Round your answer to 1 decimal place. =Total weight/no of fish in sample

_
`(15.9)/(6) =2.65`_____ pounds

(b) If 6 bass are randomly selected from Clear Lake, find the probability that the mean weight is greater than the mean of those you caught. Round your answer to 4 decimal places.

___P(mean >2.65)=
`P(Z>(2.65-2.2)/((0.6)/(√(0.6) ) ) \\=P(Z>0.18)\\=0.5-0.0714=0.4286`_____

Sample mean follows a normal distribution with mean = 2.2 and std error = 0.6/sqrt 6

(c) Which statement best describes your situation?

_____ This is not particularly unusual because the mean weight of your fish is only 0.5 pounds above the population average.