Question

The mean incubation time of fertilized eggs is 21 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day.

​(a) Determine the 20th percentile for incubation times. ​

(b) Determine the incubation times that make up the middle 39​%.

Answer 1

solution:

Given that,

mean = = 21

standard deviation = = 1

Using standard normal table,

P(Z < z) = 20%

= P(Z < z) = 0.20  

z = -0.84 Using standard normal table,

Using z-score formula  

x= z * +

x= -0.84*1+21

x= 20.16

b.

middle 39% of score is

P(-z < Z < z) = 0.39

P(Z < z) - P(Z < -z) = 0.39

2 P(Z < z) - 1 = 0.39

2 P(Z < z) = 1 + 0.39 = 1.39

P(Z < z) = 1.39/ 2 = 0.695

P(Z <0.51 ) = 0.695

z  ± 0.51 using z table

Using z-score formula  

x=± z * +

x= ±0.51*1+21

x= 20.49 , 21.51