Question

3. Suppose you work for the Ford Motor Company and must establish regulations concerning the maximum number of people who can ride in a minivan. Ford tells you that the total number of people in a minivan follows a normal distribution with a mean of 6 and a standard deviation of 2.
a. What is the probability that the total number of people in the van is between 2 and 4 people?
b. What is the probability that the total number of people in the van is between 5 and 7 people?
c. What is the probability that the total number of people in the van is greater than 10 people?

Answer 1

Here the distribution ~N(6,2²), i.e. mean=6, variance = 2²=4.

Standardize the given variable to Z and look up probabilities from the normal distribution table.