The weights of pink salmon in a fishery are normally distributed, with a mean of 3.25 pounds and a standard deviation of 0.25 pounds.
what is the probability that a salmon weighs between 2.95 pounds and 3.95 pounds?
a) 0.12
b) 0.38
c) 0.62
d) 0.88

0.88

Step-by-step explanation:

Given : The weights of pink salmon in a fishery are normally distributed, with a mean of 3.25 pounds and a standard deviation of 0.25 pounds.

To Find :  What is the probability that a salmon weighs between 2.95 pounds and 3.95 pounds?

Solution:

We will use z score to find  the probability that a salmon weighs between 2.95 pounds and 3.95 pounds

Formula :

At x = 2.95

Refer the z table for p value

P(Z<-1.2) =0.1151

At x = 3.95

Refer the z table for p value

P(Z<2.8) =0.9974

P(2.95<x<3.95)=P(-1.2<z<2.8)=P(z<2.8)-P(z<-1.2) = 0.9974-0.1151 = 0.88

Hence the probability that a salmon weighs between 2.95 pounds and 3.95 pounds is 0.88

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