125. Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
a) 5 days b) 45 days c) 65 days d) 81 days ANSWER:
d
TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, mean
126. A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?
a) 0.0256 b) 0.0625 c) 0.16 d) 1.00 ANSWER:
b
TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution
127. A probability distribution is an equation that
a) associates a particular probability of occurrence with each outcome in the sample space.
b) measures outcomes and assigns values of X to the simple events.
c) assigns a value to the variability in the sample space.
d) assigns a value to the center of the sample space.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate KEYWORDS: probability distribution
128. The connotation "expected value" or "expected gain" from playing roulette at a casino means a) the amount you expect to "gain" on a single play.
b) the amount you expect to "gain" in the long run over many plays.
c) the amount you need to "break even" over many plays.
d) the amount you should expect to gain if you are lucky.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy KEYWORDS: expected value
129. Which of the following about the binomial distribution is not a true statement?
a) The probability of success must be constant from trial to trial.
b) Each outcome is independent of the other.
c) Each outcome may be classified as either "success" or "failure."
d) The random variable of interest is continuous.
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: binomial distribution, properties 130. In a binomial distribution
a) the random variable X is continuous.
b) the probability of success p is stable from trial to trial.
c) the number of trials n must be at least 30.
d) the results of one trial are dependent on the results of the other trials.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: binomial distribution, properties
131. Whenever p = 0.5, the binomial distribution will a) always be symmetric.
b) be symmetric only if n is large.
c) be right-skewed.
d) be left-skewed.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
132. Whenever p = 0.1 and n is small, the binomial distribution will be a) symmetric.
b) right-skewed.
c) left-skewed.
d) None of the above.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
133. If n = 10 and p = 0.70, then the mean of the binomial distribution is a) 0.07
b) 1.45.
c) 7.00 d) 14.29 ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: binomial distribution, mean
134. If n = 10 and p = 0.70, then the standard deviation of the binomial distribution is a) 0.07
b) 1.45 c) 7.00 d) 14.29 ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: binomial distribution, standard deviation
135. If the outcomes of a random variable follow a Poisson distribution, then their a) mean equals the standard deviation.
b) median equals the standard deviation.
c) mean equals the variance.
d) median equals the variance.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: Poisson distribution, mean, standard deviation, properties
136. What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem?
An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims. It is known that the industry proportion for false claims is 3%. The consulting firm has decided to randomly and independently sample 100 of the company’s insurance claims.
They believe the number of these 100 that are false will yield the information the company desires.
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
a
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: binomial distribution, properties 137. The covariance
a) must be between -1 and +1.
b) must be positive.
c) can be positive or negative.
d) must be less than +1.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy KEYWORDS: covariance, properties
138. What type of probability distribution will most likely be used to analyze warranty repair needs on new cars in the following problem?
The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days.
Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
a
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: binomial distribution, properties
139. What type of probability distribution will most likely be used to analyze the number of chocolate chip parts per cookie in the following problem?
The quality control manager of Marilyn’s Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0. The manager is interested in analyzing the probability that any particular cookie being inspected has fewer than 5.0 chip parts.
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
140. What type of probability distribution will most likely be used to analyze the number of cars with defective radios in the following problem?
From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. The sales manager of one dealership wants to predict the probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios.
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution, properties
141. A stock analyst was provided with a list of 25 stocks. He was expected to pick 3 stocks from the list whose prices are expected to rise by more than 20% after 30 days. In reality, the prices of only 5 stocks would rise by more than 20% after 30 days. If he randomly selected 3 stocks from the list, he would use what type of probability distribution to compute the probability that all of the chosen stocks would appreciate more than 20%
after 30 days?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution, properties
142. A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
143. A company has 125 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 20 of the computers will require repair on a given day, one will use what type of probability distribution?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties 144. The portfolio expected return of two investments
a) will be higher when the covariance is zero.
b) will be higher when the covariance is negative.
c) will be higher when the covariance is positive.
d) does not depend on the covariance.
ANSWER:
d
TYPE: MC DIFFICULTY: Easy KEYWORDS: portfolio, mean
145. A financial analysis is presented with information on the past records of 60 start-up companies and told that in fact only 3 of them have managed to become highly successful. He selected 3 companies from this group as the candidates for success. To analyze his ability to spot the companies that will eventually become highly successful, he will use what type of probability distribution?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution, properties
146. On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store.
What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
147. A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What type of probability distribution can be used to figure out his chance of getting at least 20 questions right?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
148. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.
Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value.
a) Most of the weeks resulted in rat costs of $13.00.
b) The median cost for the distribution of rat costs is $13.00.
c) The expected or average cost for all weekly rat purchases is $13.00.
d) The rat cost that occurs more often than any other is $13.00.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy KEYWORDS: mean
149. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.
Prices for 100 rats follow the following distribution:
Price: $10.00 $12.50 $15.00 Probability: 0.35 0.40 0.25
How much should the lab budget for next year’s rat orders be, assuming this distribution does not change?
a) $520 b) $637 c) $650 d) $780 ANSWER:
b
TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean
150. The local police department must write, on average, 5 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) If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.
d) The mean has no interpretation since 0.5 ticket can never be written.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: mean, Poisson distribution
151. True or False: The Poisson distribution can be used to model a continuous random variable.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Poisson distribution, properties
152. True or False: Another name for the mean of a probability distribution is its expected value.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy KEYWORDS: mean
153. True or False: The number of customers arriving at a department store in a 5-minute period has a binomial distribution.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Poisson distribution, properties
154. True or False: The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Poisson distribution, properties
155. True or False: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution, properties
156. True or False: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution, properties
157. True or False: The diameters of 10 randomly selected bolts have a binomial distribution.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: binomial distribution, properties
158. True or False: The largest value that a Poisson random variable X can have is n.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
159. True or False: In a Poisson distribution, the mean and standard deviation are equal.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
160. True or False: In a Poisson distribution, the mean and variance are equal.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
161. True or False: If p remains constant in a binomial distribution, an increase in n will increase the variance.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
162. True or False: If p remains constant in a binomial distribution, an increase in n will not change the mean.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
163. True or False: Suppose that a judge’s decisions follow a binomial distribution and that his verdict is correct 90% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: binomial distribution, probability
164. True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The average number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.0504.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Poisson distribution, probability
165. True or False: The covariance between two investments is equal to the sum of the variances of the investments.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy KEYWORDS: covariance, variance
166. True or False: If the covariance between two investments is zero, the variance of the sum of the two investments will be equal to the sum of the variances of the investments.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy KEYWORDS: covariance, variance
167. True or False: The expected return of the sum of two investments will be equal to the sum of the expected returns of the two investments plus twice the covariance between the investments.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate KEYWORDS: mean, portfolio
168. True or False: The variance of the sum of two investments will be equal to the sum of the variances of the two investments plus twice the covariance between the investments.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate KEYWORDS: covariance, variance
169. True or False: The variance of the sum of two investments will be equal to the sum of the variances of the two investments when the covariance between the investments is zero.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate KEYWORDS: covariance, variance
170. True or False: The expected return of a two-asset portfolio is equal to the product of the weight assigned to the first asset and the expected return of the first asset plus the product of the weight assigned to the second asset and the expected return of the second asset.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy KEYWORDS: mean, portfolio
TABLE 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.
171. Referring to Table 5-1, the probability that both sound an alarm in the presence of smoke is ________.
ANSWER:
0.64
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
172. Referring to Table 5-1, the probability that neither sound an alarm in the presence of smoke is ________.
ANSWER:
0.04
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
173. Referring to Table 5-1, the probability that at least one sounds an alarm in the presence of smoke is ________.
ANSWER:
0.96
TYPE: FI DIFFICULTY: Difficult KEYWORDS: binomial distribution TABLE 5-2
A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).
174. Referring to Table 5-2, the probability that all 3 businesses succeed is ________.
ANSWER:
0.216
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
175. Referring to Table 5-2, the probability that all 3 businesses fail is ________.
ANSWER:
0.064
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
176. Referring to Table 5-2, the probability that at least 1 business succeeds is ________.
ANSWER:
0.936
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
177. Referring to Table 5-2, the probability that exactly 1 business succeeds is ________.
ANSWER:
0.288
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
178. If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ . ANSWER:
0.4116
TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution
179. If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________ . ANSWER:
0.3483
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
180. If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________ . ANSWER:
0.0729
TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution
181. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 1 prefers brand C is ________.
ANSWER:
0.0768
TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution
182. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that at least 1 prefers brand C is ________.
ANSWER:
0.9898
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
183. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 3 prefer brand C is ________.
ANSWER:
0.3456
TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution
184. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 4 prefer brand C is ________.
ANSWER:
0.2592
TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution
185. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that at most 2 prefer brand C is ________.
ANSWER:
0.3174
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
186. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that more than 3 prefer brand C is ________.
ANSWER:
0.3370
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
187. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that less than 2 prefer brand C is ________.
ANSWER:
0.0870
TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution
188. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The average number that you would expect to prefer brand C is ________.
ANSWER:
3
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution, mean
189. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The variance of the number that prefer brand C is ________.
ANSWER:
1.2
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution, variance TABLE 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.
X 0 1 2 3
P(X )
0.35 0.35 0.25 0.05
190. Referring to Table 5-3, the probability of no retransmissions is ________.
ANSWER:
0.35
TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution
191. Referring to Table 5-3, the probability of at least one retransmission is ________.
ANSWER:
0.65
TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution
192. Referring to Table 5-3, the mean or expected value for the number of retransmissions is ________.
ANSWER:
1.0
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, mean
193. Referring to Table 5-3, the variance for the number of retransmissions is ________.
ANSWER:
0.80
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, variance
194. Referring to Table 5-3, the standard deviation of the number of retransmissions is ________.
ANSWER:
0.894
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, standard deviation
195. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The
195. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The