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The weight of fish in Lake Paradise follows a normal distribution with mean of 7

ID: 3174096 • Letter: T

Question

The weight of fish in Lake Paradise follows a normal distribution with mean of 7.5 lbs and standard deviation of 2 lbs.

a. What proportion of fish are between 9 lbs and 12 lbs? Give your answer to 3 decimal places.

b. Alex boasts that he once caught a fish that was just big enough to be in the top 4% of of the fish population. How much did his fish weigh? Give your answer to 2 decimal places.

c. If one catches a fish from the bottom 20% of the population, the fish must be returned to the lake. What is the weight of the smallest fish that one can keep? Give your answer to 2 decimal places.

Explanation / Answer

Mean = 7.5

Stdev = 2

a. P(9<X<12) = P(-.75<Z<2.25) = .9878-.2266 = .7612

b. Z value for top 4% is 1.75

So, 7.5+2*1.75 = 11 lbs

c. This is a Z value of -.84

Weught of bottom 20% = 7.5 - .84*1.75 = 6.03 lbs