Question

The number of pizzas consumed per month by university students is normally distributed with a mean of 14 and a standard deviation of 4.

B. What is the probability that in a random sample of size 8, a total of more than 104 pizzas are consumed? (Hint: What is the mean number of pizzas consumed by the sample of 8 students?)

Answer 1

The probability that a total of more than 104 pizzas are consumed is 0

What is the probability a total of more than 104 pizzas are consumed?

From the question, we have the following parameters that can be used in our computation:

Population mean = 14

Population standard deviation = 4

The sample mean is always equal to the population mean

So, we have

Mean = 14

For the sample standard deviation, we have

SD = SD population/√n

So, we have

SD = 4/√8

Evaluate

SD = 1.41

The standard score for 104 pizza is represented as

z = (Score - Mean)/SD

So, we have

z = (104 - 14)/1.41

Evaluate

z = 63.82

So, the probability is represented as

P(x > 104) = P(z > 63.82)

Using the z-table of probabilities, we have

P(x > 104) = 0

Hence, the probability is 0