Question

The cholesterol content of large chicken eggs is normally distributed with a mean of 187 milligrams and standard deviation 15 milligrams.

Use this information to answer the below by filling in the blanks.

a. What is the probability one of these eggs is between 186 and 200?

b. Seventy-five percent of these eggs have cholesterol content less than ______

Answer 1

Solution :

Given that ,

mean =   = 187

standard deviation = =15

(A)

P(186< x <200 ) = P[(186-187) /15 < (x - ) / < (200-187) /15 )]

= P( -0.07< Z <0.87 )

= P(Z <0.87 ) - P(Z <-0.07)

Using z table   

= 0.8078-0.4721

probability= 0.3357

(B)

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.67 ) = 0.75

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 15+187

x = 197.05