Download CHAPTER 7 SECTION 5: RANDOM VARIABLES AND DISCRETE

CHAPTER 7 SECTION 5: RANDOM VARIABLES AND DISCRETE
PROBABILITY DISTRIBUTIONS
MULTIPLE CHOICE
235. The Poisson random variable is a:
a. discrete random variable with infinitely many possible values.
b. discrete random variable with finite number of possible values.
c. continuous random variable with infinitely many possible values.
d. continuous random variable with finite number of possible values.
ANS: A
PTS: 1
REF: SECTION 7.5
236. Given a Poisson random variable X, where the average number of successes occurring in a specified
interval is 1.8, then P(X = 0) is:
a. 1.8
b. 1.3416
c. 0.1653
d. 6.05
ANS: C
PTS: 1
REF: SECTION 7.5
237. Which of the following cannot have a Poisson distribution?
a. The length of a movie.
b. The number of telephone calls received by a switchboard in a specified time period.
c. The number of customers arriving at a gas station in Christmas day.
d. The number of bacteria found in a cubic yard of soil.
ANS: A
PTS: 1
REF: SECTION 7.5
238. In a Poisson distribution, the:
a. mean equals the standard deviation.
b. median equals the standard deviation.
c. mean equals the variance.
d. None of these choices.
ANS: C
PTS: 1
REF: SECTION 7.5
239. Big Rapids local police department must write, on average, 6 tickets a day to keep department
revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson
distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.
a. The number of tickets that is written most often is 6.5 tickets per day.
b. Half of the days have less than 6.5 tickets written and half of the days have more than 6.5
tickets written.
c. The expected number of tickets written would be 6.5 per day.
d. The mean has no interpretation.
ANS: C
PTS: 1
REF: SECTION 7.5
240. A community college has 150 personal computers. The probability that any one of them will require
repair on a given day is 0.025. To find the probability that exactly 25 of the computers will require
repair, one will use what type of probability distribution?
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a.
b.
c.
d.
Binomial distribution
Poisson distribution
Normal distribution
None of these choices.
ANS: A
PTS: 1
REF: SECTION 7.5
241. On the average, 1.6 customers per minute arrive at any one of the checkout counters of Meijer grocery
store. What type of probability distribution can be used to find out the probability that there will be no
customers arriving at a checkout counter in 10 minutes?
a. Binomial distribution
b. Poisson distribution
c. Normal distribution
d. None of these choices.
ANS: B
PTS: 1
REF: SECTION 7.5
TRUE/FALSE
242. The Poisson distribution is applied to events for which the probability of occurrence over a given span
of time, space, or distance is very small.
ANS: T
PTS: 1
REF: SECTION 7.5
243. The Poisson random variable is a discrete random variable with infinitely many possible values.
ANS: T
PTS: 1
REF: SECTION 7.5
244. The mean of a Poisson distribution, where  is the average number of successes occurring in a
specified interval, is .
ANS: T
PTS: 1
REF: SECTION 7.5
245. The number of accidents that occur at a busy intersection in one month is an example of a Poisson
random variable.
ANS: T
PTS: 1
REF: SECTION 7.5
246. The Poisson probability distribution is a continuous probability distribution.
ANS: F
PTS: 1
REF: SECTION 7.5
247. The number of customers arriving at a department store in a 5-minute period has a Poisson
distribution.
ANS: T
PTS: 1
REF: SECTION 7.5
248. The number of customers making a purchase out of 30 randomly selected customers has a Poisson
distribution.
ANS: F
PTS: 1
REF: SECTION 7.5
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copied, or distributed without the prior consent of the publisher.
249. The largest value that a Poisson random variable X can have is n.
ANS: F
PTS: 1
REF: SECTION 7.5
250. In a Poisson distribution, the mean and standard deviation are equal.
ANS: F
PTS: 1
REF: SECTION 7.5
251. In a Poisson distribution, the mean and variance are equal.
ANS: T
PTS: 1
REF: SECTION 7.5
252. In a Poisson distribution, the variance and standard deviation are equal.
ANS: F
PTS: 1
REF: SECTION 7.5
COMPLETION
253. In a Poisson experiment, the number of successes that occur in any interval of time is
____________________ of the number of success that occur in any other interval.
ANS: independent
PTS: 1
REF: SECTION 7.5
254. In a(n) ____________________ experiment, the probability of a success in an interval is the same for
all equal-sized intervals.
ANS: Poisson
PTS: 1
REF: SECTION 7.5
255. In a Poisson experiment, the probability of a success in an interval is ____________________ to the
size of the interval.
ANS: proportional
PTS: 1
REF: SECTION 7.5
256. In Poisson experiment, the probability of more than one success in an interval approaches
____________________ as the interval becomes smaller.
ANS:
zero
0
PTS: 1
REF: SECTION 7.5
257. A Poisson random variable is the number of successes that occur in a period of
____________________ or an interval of ____________________ in a Poisson experiment.
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ANS: time; space
PTS: 1
REF: SECTION 7.5
258. The ____________________ of a Poisson distribution is the rate at which successes occur for a given
period of time or interval of space.
ANS:
mean
expected value
PTS: 1
REF: SECTION 7.5
259. In the Poisson distribution, the mean is equal to the ____________________.
ANS: variance
PTS: 1
REF: SECTION 7.5
260. In the Poisson distribution, the ____________________ is equal to the variance.
ANS: mean
PTS: 1
REF: SECTION 7.5
261. The possible values of a Poisson random variable start at ____________________.
ANS:
zero
0
PTS: 1
REF: SECTION 7.5
262. A Poisson random variable is a(n) ____________________ random variable.
ANS: discrete
PTS: 1
REF: SECTION 7.5
SHORT ANSWER
263. Compute the following Poisson probabilities (to 4 decimal places) using the Poisson formula:
a. P(X = 3), if  = 2.5
b. P(X  1), if  = 2.0
c. P(X  2), if  = 3.0
ANS:
a. 0.2138
b. 0.4060
c. 0.8009
PTS: 1
REF: SECTION 7.5
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copied, or distributed without the prior consent of the publisher.
264. Let X be a Poisson random variable with  = 6. Use the table of Poisson probabilities to calculate:
a. P(X  8)
b. P(X = 8)
c. P(X  5)
d. P(6  X  10)
ANS:
a. 0.847
b. 0.103
c. 0.715
d. 0.511
PTS: 1
REF: SECTION 7.5
265. Let X be a Poisson random variable with  = 8. Use the table of Poisson probabilities to calculate:
a. P(X  6)
b. P(X = 4)
c. P(X  3)
d. P(9  X  14)
ANS:
a. 0.313
b. 0.058
c. 0.986
d. 0.390
PTS: 1
REF: SECTION 7.5
Hotel Phone Calls
Phone calls arrive at the rate of 30 per hour at the reservation desk for a hotel.
266. {Hotel Phone Calls Narrative} Find the probability of receiving two calls in a five-minute interval of
time.
ANS:
 = 5(30/60) = 2.5; P(X = 2) = 0.2565
PTS: 1
REF: SECTION 7.5
267. {Hotel Phone Calls Narrative} Find the probability of receiving exactly eight calls in 15 minutes.
ANS:
 = 15(30/60) = 7.5; P(X = 8) = 0.1373
PTS: 1
REF: SECTION 7.5
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copied, or distributed without the prior consent of the publisher.
268. {Hotel Phone Calls Narrative} If no calls are currently being processed, what is the probability that the
desk employee can take four minutes break without being interrupted?
ANS:
 = 4(30/60) = 2.0; P(X = 0) = 0.1353
PTS: 1
REF: SECTION 7.5
Advertising Executive Phone Calls
An advertising executive receives an average of 10 telephone calls each afternoon between 2 and 4
P.M. The calls occur randomly and independently of one another.
269. {Advertising Executive Phone Calls Narrative} Find the probability that the executive will receive 13
calls between 2 and 4 P.M. on a particular afternoon.
ANS:
 = 10; P(X = 13) = 0.072
PTS: 1
REF: SECTION 7.5
270. {Advertising Executive Phone Calls Narrative} Find the probability that the executive will receive
seven calls between 2 and 3 P.M. on a particular afternoon.
ANS:
 = 5; P(X = 7) = 0.105
PTS: 1
REF: SECTION 7.5
271. {Advertising Executive Phone Calls Narrative} Find the probability that the executive will receive at
least five calls between 2 and 4 P.M. on a particular afternoon.
ANS:
 = 10; P(X  5) = 0.971
PTS: 1
REF: SECTION 7.5
Gas Station
The number of arrivals at a local gas station between 3:00 and 5:00 P.M. has a Poisson distribution
with a mean of 12.
272. {Gas Station Narrative} Find the probability that the number of arrivals between 3:00 and 5:00 P.M. is
at least 10.
ANS:
 =12; P(X  10) = 0.758
PTS: 1
REF: SECTION 7.5
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273. {Gas Station Narrative} Find the probability that the number of arrivals between 3:30 and 4:00 P.M. is
at least 10.
ANS:
 = 3; P(X  10) = 0.001
PTS: 1
REF: SECTION 7.5
274. {Gas Station Narrative} Find the probability that the number of arrivals between 4:00 and 5:00 P.M. is
exactly two.
ANS:
 = 6; P(X = 2) = 0.045
PTS: 1
REF: SECTION 7.5
275. Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. If the
average number of airplanes arriving per minute is 3, what is the probability that exactly 6 planes
arrive in the next minute?
ANS:
0.0504
PTS: 1
REF: SECTION 7.5
Power Outages
The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6
outages per year.
276. {Power Outages Narrative} Find the probability that there will be exactly 3 power outages in a year.
ANS:
0.0892
PTS: 1
REF: SECTION 7.5
277. {Power Outages Narrative} Find the probability that there will be at least 3 power outages in a year.
ANS:
0.9380
PTS: 1
REF: SECTION 7.5
278. {Power Outages Narrative} Find the probability that there will be at least 1 power outage in a year.
ANS:
0.9975
PTS: 1
REF: SECTION 7.5
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copied, or distributed without the prior consent of the publisher.
279. {Power Outages Narrative} Find the probability that there will be no more than 1 power outage in a
year.
ANS:
0.0174
PTS: 1
REF: SECTION 7.5
280. {Power Outages Narrative} Find the variance of the number of power outages in one year.
ANS:
6
PTS: 1
REF: SECTION 7.5
281. {Power Outages Narrative} Find the standard deviation of the number of power outages is in one year.
ANS:
2.45
PTS: 1
REF: SECTION 7.5
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.