Exercises

Chapter 5 Review Exercises

1. TV Ratings The television show Cold Case has a 15 share, meaning that while it is

being broadcast, 15% of the TV sets in use are tuned to Cold Case (based on data from Nielsen Media Research). A special focus group consists of 10 randomly selected households (each with one TV set in use during the time of a Cold Case broadcast).

a) In such groups of 10, what is the mean number of sets tuned to Cold Case?

b) In such groups of 10, what is the standard deviation for the number of sets tuned to Cold

Case?

c) For such a group of 10, find the probability that exactly 3 TV sets are tuned to Cold

Case.

d) For such a group of 10, would it be unusual to find that no sets are tuned to Cold Case?

Why or why not?

2. Homicide Deaths In one year, there were 116 homicide deaths in Richmond, Virginia

(based on “A Classroom Note on the Poisson Distribution: A Model for Homicidal Deaths in Richmond, Va for 1991,” by Winston A. Richards in Mathematics and Computer Education). For a randomly selected day, find the probability that the number of homicide deaths is a) 0 b) 1 c) 2 d) 3 e) 4

Compare the calculated probabilities to these actual results: 268 days (no homicides); 79 days (1 homicide); 17 days (2 homicides); 1 day (3 homicides); no days with more than 3 homicides.

3. Dandelions Dandelions are studied for their effects on crop production and lawn growth.

In one region, the mean number of dandelions per square meter was found to be 7.0 (based on data from Manitoba Agriculture and Food).

a) Find the probability of no dandelions in an area of 1 m2.

b) Find the probability of at least one dandelion in an area of 1 m2. c) Find the probability of at most two dandelions in an area of 1 m2.

4. Overbooking Flights Air America has a policy of booking as many as 15 persons on an

airplane that can seat only 14. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Find the probability that if Air America books 15 persons, not enough seats will be available. Is this probability low enough so that overbooking is not a real concern for passengers?

5. Reasons for Being Fired “Inability to get along with others” is the reason cited in 15%

of worker firings (based on data from Robert Half International, Inc.). Concerned about her company’s working conditions, the personnel manager at the Boston Finance Company plans to investigate the five employee firings that occurred over the past year.

a) Assuming that the 15% rate applies, find the probability that among those five

employees, the number fired because of an inability to get along with others is at least four.

b) If the personnel manager actually does find that at least four of the firings are due to an

inability to get along with others, does this company appear to be very different from the other typical companies? Why or why not?

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