Question

The number of pizzas consumed per month by university students is normally distributed with a mean of 7 and a standard deviation of 4.

A. What proportion of students consume more than 9 pizzas per month?

Probability =

B. What is the probability that in a random sample of size 9, the mean amount of pizza consumed is more than 5 pizzas per person?

Probability =

Answer 1

Solution :

A.

P(x > 9) = 1 - P(x < 9)

= 1 - P[(x - ) / < (9 - 7) / 4)

= 1 - P(z < 0.5)

= 1 - 0.6915

= 0.3085

Probability = 0.3085

B.

= / n = 4 / 9 = 1.3333

P( > 5) = 1 - P( < 5)

= 1 - P[( - ) / < (5 - 7) / 1.3333]

= 1 - P(z < -1.50)

= 1 - 0.0668

= 0.9332

Probability = 0.9332