Download AP Stats:Chapter 2 Review Problems

AP Stats:Chapter 2 Review Problems
1. Scores on the ACT college entrance exam follow a bell-shaped distribution with mean 18 and
standard deviation 6. Bob’s standardized score on the ACT was -0.7. What was Bob’s actual
ACT score?
2. Ryan has an average bowling score of 180 and bowls in a league where the average for all
bowlers is 150 and the standard deviation is 20. Bill has an average bowling score of 190 and
bowls in a league where the average is 160 and the standard deviation is 15. Who ranks higher in
his own league, Ryan or Bill?
3. Find the value z from the standard Normal distribution that satisfies each of the following
conditions. In each case sketch a standard Normal curve with your value of z marked on the axis.
a. The 12th percentile
b. 33% of all observations are greater than z
c. The 65th percentile
d. 89% of all observations are less than z
4. At some fast-food restaurants, customers who want a lid for their drinks get them from a large
stack left near straws, napkins, and condiments. The lids are made with a small amount of
flexibility so they can be stretched across the mouth of the cup and then snuggly secured. When
lids are too small or too large, customers can get very frustrated, especially if they end up spilling
their drinks. At one particular restaurant, large drink cups require lids with a diameter between
3.95 and 4.05 inches. The restaurant’s lid supplier claims that the mean diameter of their large
lids is 3.98 inches with a standard deviation of 0.02 inches. Assume that the supplier’s claim is
true.
a. What percent of large lids are too small to fit?
b. What percent of large lids are too big to fit?
c. Compare your answers to (a) and (b). Does it make sense for the lid manufacturer to try
to make one of these values larger than the other? Why or why not?
5. The deciles of any distribution are the points that mark off the lowest 10% and the highest 10%.
a. What are the deciles of the standard Normal distribution?
b. The heights of young women are approximately Normal with mean 64.5 inches and
standard deviation 2.5 inches. What are the deciles of this distribution?
6. An airline flies the same route at the same time each day. The flight time varies according to a
Normal distribution with unknown mean and standard deviation. On 15% of days, the flight
takes more than an hour. On 3% of days, the flight lasts 75 minutes or more. Determine the
mean and standard deviation
7. Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year
period. The distribution of birth weights is Normal with a mean of 3668 grams and a standard
deviation of 511 grams. Babies that weigh less than 2500 grams at birth are considered as “low
birth weight.”
a. What percent of babies will be identified as low birth weight?
b. Find the quartiles of the birth weight distribution.