Question

Suppose you own a publishing company. The daily production of books/magazines approximately follows normally distribution with a mean of 5,500 books/magazines per day with a standard deviation of 800 books/magazines per day.

A) Find 'a' such that, P(x>a) = 0.8997

B) Find 'a' such that, P(x<a) = 0.8888

Answer 1

Given,

= 5500 , = 800

We convert this to standard normal as

P(X < x) = P(Z < (x - ) / )

a)

P(X > a) = 0.8997

P(X < a) = 1 - 0.8997

P(X < a) = 0.1003

P(Z < (a - ) / ) ) = 0.1003

From Z table, z-score for the pobability of 0.1003 is -1.28

(a - ) / = -1.28

(a - 5500) / 800 = -1.28

Solve for a

a = 4476

b)

P(X < a) = 0.8888

P(Z< (a - ) / ) ) = 0.8888

From Z table, z-score for the pobability of 0.1003 is 1.22

(a - ) / = 1.22

(a - 5500) / 800 = 1.22

Solve for a

a = 6476