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AP Statistics
7.3 Sample Means
Name ____________________
1. A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain
300 milliliters (ml). In fact, the contents vary according to a normal distribution with mean   298 ml and
standard deviation   3 ml.
A. What is the probability that an individual bottle contains less than 295 ml?
B. What is the probability that the mean contents of the bottles in a six-pack is less than 295 ml?
2. A company that owns and services a fleet of cars for its sales force has found that the service lifetime of disc
brake pads varies from car to car according to a normal distribution with mean   55,000 miles and standard
deviation   4500 miles. The company installs a new brand of brake pads on 8 cars.
A. If the new brand has the same lifetime distribution as the previous type, what is the distribution of the
sample mean lifetime for the 8 cars?
B. The average life of the pads on these 8 cars turns out to be x  51,800 miles. What is the probability that
the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged?
3. The number of traffic accidents per week at an intersection varies with mean 2.2 and standard deviation 1.4.
The number of accidents in a week must be a whole number, so the population distribution is not normal.
A. Let x be the number of accidents per week at the intersection during a year (52 weeks). What is the
approximate distribution of x according to the central limit theorem?
B. What is the approximate probability that x is less than 2?
C. What is the approximate probability that there are fewer than 100 accidents at the intersection in a year?
4. The composite score of individual students on the ACT college entrance examination in 2009 followed a
Normal distribution with mean 21.1 and standard deviation 5.1
A. What is the probability that a single student randomly chosen from all those taking the test scores 23 or
higher? Show your work.
B. Now take an SRS of 50 students who took the test. What is the probability that the mean score x of these
students is 23 or higher? Show your work.
5. Investors remember 1987 as the year stocks lost 20% of their value in a single day. For 1987, as a whole, the
mean return of all common stocks on the New York Stock Exchange was   3.5%. (That is, these stocks
lost an average of 3.5% of their value in 1987.) The standard deviation of the returns was about   26%.
A. Assuming that the population distribution of returns on individual common stocks is normal, what is the
probability that a randomly chosen stock showed a return of at least 5% in 1987?
B. Assuming that the population distribution of returns on individual common stocks is normal, what is the
probability that a randomly chosen portfolio of 5 stocks showed a return of at least 5% in 1987?
C. What percentage of 5-stock portfolios lost money in 1987?