The bass in Clear Lake have weights that are normally distributed with a mean of

Question

The bass in Clear Lake have weights that are normally distributed with a mean of 2.4 pounds and a standard deviation of 0.8 pounds.

(a) Suppose you only want to keep fish that are in the top 20% as far as weight is concerned. What is the minimum weight of a keeper? Round your answer to 2 decimal places. pounds

(b) Suppose you want to mount a fish if it is in the top 0.5% of those in the lake. What is the minimum weight of a bass to be mounted? Round your answer to 2 decimal places. pounds

(c) Determine the weights that delineate the middle 95% of the bass in Clear Lake. Round your answers to 2 decimal places. from to pounds

Explanation / Answer

= 2.4, = 0.8

(a) Area under the standard normal curve is 0.20 to the right of z = 0.8416

x = + z * = 2.4 + 0.8416 * 0.8 = 3.07 pounds

(b) Area under the standard normal curve is 0.005 to the right of z =2.5758

x = + z * = 2.4 + 2.5758 * 0.8 = 4.46 pounds

(c) Here, z = 1.96

x = + z * = 2.4 + 1.96 * 0.8 = 3.97 pounds.

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