INTERNATIONAL UNIVERSITY
Semester 1, Academic Year 2018-2019 TUTORIAL MATERIAL
Discrete Random Variables
1. Lee Iacocca volunteered to drive one of his Chryslers into a brick wall to demonstrate the
effectiveness of airbags used in these cars. Airbags are known to activate at random when the car
decelerates anywhere from 9 to 14 miles per hour per second (mph/s). The probability distribution
for the deceleration speed at which bags activate is given below. Mph/s Probability 9 0.12 10 0.23 11 0.34 12 0.21 13 0.06 14 0.04 a.
If the airbag activates at a deceleration of 12 mph/s or more, Iacocca would get hurt. What is the
probability of his being hurt in this demonstration? b.
What is the expected deceleration at airbag activation moment? c.
What is the standard deviation of deceleration at airbag activation time?
2. A major ski resort in the eastern United States closes in late May. Closing day varies from year to
year depending on when the weather becomes too warm for making and preserving snow. The day in
May and the number of years in which closing occurred that day are reported in the table: Day Number of Years 21 2 22 5 23 1 24 3 25 3 26 1 27 2 28 1 a.
Based only on this information, estimate the probability that you could not ski at this resort after May 25 next year. b.
What is the average closing day based on history?
3. The number of orders for installation of a computer information system arriving at an agency per
week is a random variable X with the following probability distribution: a.
What is the probability that either four or five orders will arrive in a given week? b.
Find the expected the number of weekly orders. c.
Find the standard deviation of the number of weekly orders.
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Semester 1, Academic Year 2018-2019 X P(X) 0 0.1 1 0.20 2 0.30 3 0.15 4 0.15 5 0.05 6 0.05
4. The Bombay Company offers reproductions of classic 18th- and 19th-century English furniture
pieces, which have become popular in recent years. The following table gives the probability
distribution of the number of Raffles tables sold per day at a particular Bombay store.
a. Find the probability that at most five tables will be sold tomorrow.
b. What is the expected number of tables sold per day?
c. Find the variance and the standard deviation of the number of tables sold per day. Number of table Probability 0 0.05 1 0.05 2 0.10 3 0.15 4 0.20 5 0.15 6 0.15 7 0.10 8 0.05
5. In the Ardmore Hotel, 20 percent of the customers pay by American Express credit card. (a) Of the
next 10 customers, what is the probability that none pay by American Express? (b) At least two? (c)
Fewer than three? (d) What is the expected number who pay by American Express? (e) Find the standard deviation.
6. Historically, 5 percent of a mail-order firm’s repeat charge-account customers have an incorrect
current address in the firm’s computer database. (a) What is the probability that none of the next 12
repeat customers who call will have an incorrect address? (b) One customer? (c) Two customers? (d) Fewer than three?
7. At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic
beverage is 0.38. Use Excel to find the probability that in a sample of 5 customers (a) none of the 5
will order a nonalcoholic beverage, (b) at least 2 will, (c) fewer than 4 will, (d) all 5 will order a nonalcoholic beverage.
8. J.D. Power and Associates says that 60 percent of car buyers now use the Internet for research and
price comparisons. (a) Find the probability that in a sample of 8 car buyers, all 8 will use the
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INTERNATIONAL UNIVERSITY
Semester 1, Academic Year 2018-2019
Internet; (b) at least 5; (c) more than 4. (d) Find the mean and standard deviation of the probability distribution.
9. There is a 70 percent chance that an airline passenger will check bags. In the next 16 passengers that
check in for their flight at Denver International Airport, find the probability that (a) all will check
bags; (b) fewer than 10 will check bags; (c) at least 10 will check bags. 10.
Police records in the town of Saratoga show that 15 percent of the drivers stopped for speeding
have invalid licenses. If 12 drivers are stopped for speeding, find the probability that (a) none will
have an invalid license; (b) exactly one will have an invalid license; (c) at least 2 will have invalid licenses. 11.
Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the
probability that of 24 randomly selected patients: a. 4 will recover? b. At most 6 will recover? c. At least 20 will die? d. All will recover? 12.
According to J.D. Power and Associates’ 2006 Initial Quality Study, consumers reported on
average 1.7 problems per vehicle with new 2006 Volkswagens. In a randomly selected new
Volkswagen, find the probability of (a) at least one problem; (b) no problems; (c) more than three problems. 13.
At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 1.5 per
day on a typical Wednesday. Let X be the number of cancellations on a particular Wednesday. (a)
What is the probability that no cancellations will occur on a particular Wednesday? (b) One? (c)
More than two? (d) Five or more? 14.
The average number of items (such as a drink or dessert) ordered by a Noodles & Company
customer in addition to the meal is 1.4. These items are called add-ons. Define X to be the number of
add-ons ordered by a randomly selected customer. (a) What is the probability that 3 randomly
selected customers order at least 5 add-ons? (b) What is the probability that two randomly selected
customers order 2 to 5 add-ons?
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