Download MDM 4UI: 2015-2016 Unit 9 Day 4: Applications of the Normal

MDM 4UI: 2015-2016
Unit 9
Day 4: Applications of the Normal Distribution
Practice Problems
1. Two dice are rolled. A double is considered a win, and anything else is a loss. What is the minimum
number of rolls that should be made to model this situation using a normal distribution?
2. A special HOV (high occupancy vehicle) lane along a highway is reserved for the cars carrying two or
more people. Police records indicate that 8% of the cars in the HOV lane are occupied by fewer than
two people. A random check observed 100 cars.
a. Can this binomial distribution be approximated by a normal distribution?
b. Determine the mean and standard deviation of the normal approximation.
c. Determine the probability that exactly 10 of the cars contained one person.
3. A card is drawn randomly from a deck and then replaced. The deck is shuffled. Thirty trials are carried
out and the number of diamonds drawn is recorded.
a. Can this binomial distribution be approximated by a normal distribution?
b. Determine the mean and standard deviation of the normal approximation.
c. Use the normal approximation to determine the probability of getting more than 10 diamonds.
4. Microwave ovens made in China are packaged into containers and shipped to Canada. About 1% are
expected to be dented during transport. A sample of five ovens is removed from a container that holds
200. If one if found dented, the container is rejected.
a. Can this hypergeometric distribution be approximated by a normal distribution?
b. Determine the mean and standard deviation of a normal approximation to this distribution.
c. Use the normal approximation to determine the probability that no ovens in the sample are
dented.
5. An insurance company knows that 12% of the homeowners in a town of 900 are customers. The
marketing department calls 50 homes at random. What is the probability that 10 or more of these are
already customers?