Question

Thediameterofanextra-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

P(x > 27) = 1 - P(x<27 )

= 1 - P[(x -) / < (27-24) /3 ]

= 1 - P(z < 1)

Using z table

= 1 - 0.8413

probability= 0.1587

B

P(Z > z) = 75%

= 1 - P(Z < z) = 0.75  

= P(Z < z) = 1 - 0.75

= P(Z < z ) = 0.25

z = -0.67 ( using z table )

Using z-score formula,

x = z * +

=-0.67*3+24

=21.99

=22