Percentage of salmon in the river with the 68-95-99.7 rule

Question

The length X of salmon in a river has normal distribution with mean μ = 17 inches and standard
deviation σ = 4 inches.

 

What percent of the salmon in the river are between 9 inches and 17 inches?

 

What percent of the salmon in the river are between 17 inches and 21
inches?

Answer 1

Prob( 9 < x < 17) = Prob (  (9-17)/4 < z < (17-17)/4 ) = Prob ( -2 < x < 0)

         = Prob (x<0) - Prob(x<-2) = 0.5 - 0.0228 = 0.4772

 

Prob ( 17 < x < 21) = Prob( 0 < z < 4) = prob ( x<4) - Prob(x<0) = 1 - 1/2 = 1/2