Bass: The bass in Clear Lake have weights that are normally distributed with a m

Question

Bass: The bass in Clear Lake have weights that are normally distributed with a mean of 2.1 pounds and a standard deviation of 0.6 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

a) From z table,

P(z > 0.84) = 0.20

Hence,

Minimum weight required = 2.1 + 0.84*0.6 = 2.60

b) From z table,

P(z > 2.58) = 0.005

Hence,

Minimum weight required = 2.1 + 2.58*0.6 = 3.65

c) From z table,

P(-1.96 < z < 1.96) = 0.95

Hence,

Middle 95% weights will lie between:

2.1 - 1.96(0.6) to 2.1 + 1.96(0.6)

0.92 to 3.28

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