MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

Answer:0.88Step-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 poundsFormula : [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 valueP(Z<-1.2) =0.1151At x = 3.95[tex]z=\frac{3.95-3.25}{0.25}[/tex][tex]z=2.8[/tex]Refer the z table for p valueP(Z<2.8) =0.9974P(2.95<x<3.95)=P(-1.2<z<2.8)=P(z<2.8)-P(z<-1.2) = 0.9974-0.1151 = 0.88Hence the probability that a salmon weighs between 2.95 pounds and 3.95 pounds is 0.88