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 2.5 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 90% of the bass in Clear Lake. Round your answers to 2 decimal places.

from ______ to ______ pounds

Explanation / Answer

We are using Z table for reference to get over this question.

Here' it is incase you need it: http://sixsigmastudyguide.com/wp-content/uploads/2014/04/z-table.jpg

Params of Normal distribution are given below:

Mean = 2.5

Stdev = .8

a. P(X>=x) = .2

P(Z>= x-2.5/.8) = .2

So, we see that Z corresponding to this +.84

x-2.5/.8 = .84

x = .84*.8+2.5 = 3.172

Answer is 3.172 pounds

b.

P(Z>= x-2.5/.8) = .05

x = 2.575*.8+2.5 = 4.56

Answer is 4.56 pounds

c.

P(-z<Z<+z) = .90

z value such that .90 of area is around mean is -1.645 and 1.645

or the in pounds the same is :

-1.645*.8+2.5 = to 1.645*.8+2.5

1.184 pounds to 3.816 pounds

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