1) Waiting in Line: A Wendy's manager performed a study to determine a probability distribution for the number of people, X, waiting in line during lunch. The results were as follows:
(a) Verify that this is a discrete probability distribution.
(c) Compute and interpret the mean of the random variable X.
(d) Compute the standard deviation of the random variable X.
(e) What is the probability that eight people are waiting in line for lunch?
2) Smokers: According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.
(a) Explain why this is a binomial experiment.
(b) Find and interpret the probability that exactly 8 of them started smoking before 21 years of age.
(c) Find and interpret the probability that fewer than 8 of them started smoking before 21 years of age.
(d) Find and interpret the probability that at least 8 of them started smoking before 21 years of age.
(e) Find and interpret the probability that between 7 and 9 of them, inclusive, started smoking before 21 years of age.
3) You Explain It! Miles per Gallon: Elena conducts an experiment in which she ?lls up the gas tank on her Toyota Camry 40 times and records the miles per gallon for each ?ll-up. A histogram of the miles per gallon indicates that a normal distribution with a mean of 24.6 miles per gallon and a standard deviation of 3.2 miles per gallon could be used to model the gas mileage for her car.
(a) The ?gure represents the normal curve with m = 24.6 miles per gallon and s = 3.2 miles per gallon. The area under the curve to the right of x = 26 is 0.3309. Provide two interpretations of this area.
(b) The ?gure at the top of the next column represents the normal curve with m = 24.6 miles per gallon and s = 3.2 miles per gallon. The area under the curve between x = 18 and x = 21 is 0.1107. Provide two interpretations of this area.
4) Assume that the random variable X is normally distributed, with mean m = 50 and standard deviation s = 7. Find the 90th percentile for X.
5) Smokers: According to the Information Please Almanac, 80% of adult smokers started smoking before they were 18 years old. Suppose 100 smokers 18 years old or older are randomly selected. Use the normal approximation to the binomial to:
(a) approximate the probability that exactly 80 of them started smoking before they were 18 years old.
(b) approximate the probability that at least 80 of them started smoking before they were 18 years old.
(c) approximate the probability that fewer than 70 of them started smoking before they were 18 years old.