Question

The number of pizzas consumed per month by university students is normally distributed with a mean of 6 and a standard deviation of 4.

A. What proportion of students consume more than 7 pizzas per month?

Probability =

B. What is the probability that in a random sample of size 8, a total of more than 40 pizzas are consumed? (Hint: What is the mean number of pizzas consumed by the sample of 8 students?)

Probability =

Answer 1

Solution :

Given that ,

A) P(x > 7 ) = 1 - p( x< 7)

=1- p P[(x - ) / < (7 - 6) / 4 ]

=1- P(z < 0.25)

= 1 - 0.5987

= 0.4013

B) n = 8

= 40/ 8 = 5

= 6

= / n = 4 / 8 = 1.414

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

= 1 - P[( - ) / < (5 - 6) /1.414 ]

= 1 - P(z < -0.71)   

= 1 - 0.2389

= 0.7611