Question

The diameterofanextra-largepizzaatPopolosPizzainbeautifulFresno, CA is normally distributed with a mean μ = 24 inches and a standard deviation σ = 3 inches.

(a) Find the probability that a randomly selected extra-large pizza has a
diameter greater than 27 inches.

(b) My awesome brother Tim is delighted to have gotten an extraordinarily large pizza. A Popolos Pizza spokeswoman told him it is larger than 75% of all extra-large pizzas they make. What is the diameter of this pizza?

Answer 1

Solution :

Given that,

mean = = 24

standard deviation = = 3

a ) P (x > 27)

= 1 - P (x < 27 )

= 1 - P ( x -  / ) < ( 27 - 24 / 3)

= 1 - P ( z < 3 / 3 )

= 1 - P ( z < 1 )

Using z table

= 1 - 0.8413

= 0.1587

Probability = 0.1587

b ) P( Z > z) = 75%

P(Z > z) = 0.75

1 - P( Z < z) = 0.75

P(Z < z) = 1 - 0.75

P(Z < z) = 0.25

z = - 0.67

Using z-score formula,

x = z * +

x = -0.67 * 3 + 24

x =21.99

The diameter of pizza = 21.99