Question

The mean incubation time of fertilized eggs is 21days. Suppose the incubation times are approximately normally distributed with a standard deviation of 11day.

(b) Determine the incubation times that make up the middle 97​%.

Answer 1

Given that,

mean = = 21

standard deviation = = 11

middle 97% of score is

P(-z < Z < z) = 0.97

P(Z < z) - P(Z < -z) = 0.97

2 P(Z < z) - 1 = 0.97

2 P(Z < z) = 1 + 0.97 =1.97

P(Z < z) =1.97 / 2 = 0.985

P(Z <2.17 ) = 0.985

z  ± 2.17 using standard normal (Z) table   

Using z-score formula  

x= z * +

x= -2.17*11+21

x= 2.87

z = 2.17

Using z-score formula  

x= z * +

x= 2.17*11+21

x= 44.87