Answer:
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 : [tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]\mu = 3.25\\\sigma = 0.25[/tex]
At x = 2.95
[tex]z=\frac{2.95-3.25}{0.25}[/tex]
[tex]z=-1.2[/tex]
Refer the z table for p value
P(Z<-1.2) =0.1151
At x = 3.95
[tex]z=\frac{3.95-3.25}{0.25}[/tex]
[tex]z=2.8[/tex]
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
