Question

The mean incubation time of fertilized eggs is 21 days. Suppose the incubation times are approximately...

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​%.

Homework Answers

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

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