Question 1

Suppose that a judge's decisions follow a binomial distribution and that his verdict
is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2
incorrect verdicts is 0.736.

Accepted Answer

A) True 
 B)False

Question 2

If the outcomes of a variable follow a Poisson distribution, then their

Accepted Answer

A)  mean equals the standard deviation. 
B)  median equals the standard deviation. 
C)  mean equals the variance. 
D)  median equals the variance.

Question 3

SCENARIO 5-3
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition. The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution: 
-Referring to Scenario 5-3, what is the standard deviation of the value gain for the house in
neighborhood A?

Accepted Answer

The answer of SCENARIO 5-3
There are two houses with almost...

Question 4

SCENARIO 5-2
The following table contains the probability distribution for X = the number of traffic accidents
reported in a day in a small city in the Midwest. $$\begin{array} { c | | c | c | c | c | c | c | } 
X & 0 & 1 & 2 & 3 & 4 & 5 \
\hline P ( X ) & 0.10 & 0.20 & 0.45 & 0.15 & 0.05 & 0.05
\end{array}$$
-Referring to Scenario 5-2, the probability of 3 accidents is ________.

Accepted Answer

The answer of SCENARIO 5-2
The following table contains the probability...

Question 5

SCENARIO 5-6
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).
-Referring to Scenario 5-6, the probability that all 3 businesses fail is ________.

Accepted Answer

The answer of SCENARIO 5-6
A certain type of new business...

Question 6

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.

Accepted Answer

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 mean cost for all weekly rat purchases is $13.00. 
D)  The rat cost that occurs more often than any other is $13.00.

Question 7

If π remains constant in a binomial distribution, an increase in n will increase the
variance.

Accepted Answer

A) True 
 B)False

Question 8

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: $\begin{array}{lrrr}
\text { Price: } & \$ 10.00 & \$ 12.50 & \$ 15.00 \
\hline \text { Probability: } & 0.35 & 0.40 & 0.25
\end{array}$
 How much should the lab budget for next year's rat orders be, assuming this distribution does not
Change?

Accepted Answer

A)  $520 
B)  $637 
C)  $650 
D)  $780

Question 9

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 standard deviation of the number of times she will be audited is ________.

Accepted Answer

The answer of In a game called Taxation and Evasion,...

Question 10

If n = 10 and π = 0.70, then the mean of the binomial distribution is

Accepted Answer

A)  0.07 
B)  1.45. 
C)  7.00 
D)  14.29

Question 11

SCENARIO 5-8
The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact
fluorescent light bulbs. When the production process is in control, the mean number of bad bulbs per
shift is 6.0.
-Referring to Scenario 5-8, what is the probability that any particular shift being inspected has
produced at least 6.0 bad bulbs.

Accepted Answer

The answer of SCENARIO 5-8
The quality control manager of Green...

Question 12

A probability distribution is an equation that

Accepted Answer

A)  associates a particular probability of occurrence with each outcome. 
B)  measures outcomes and assigns values of X to the simple events. 
C)  assigns a value to the variability of the set of events. 
D)  assigns a value to the center of the set of events.

Question 13

If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .

Accepted Answer

The answer of If X has a binomial distribution with...

Question 14

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.

Accepted Answer

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.

Question 15

SCENARIO 5-5
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.
-Referring to Scenario 5-5, the probability that neither sound an alarm in the presence of smoke is
________.

Accepted Answer

The answer of SCENARIO 5-5
The probability that a particular type...

Question 16

SCENARIO 5-7
A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of
consumers from the U.S., Canada, and China who said that they planned to spend more on holiday
shopping were 40%, 34% and 73%, respectively. The survey also found that the percentage of
consumers from the U.S., Canada, and China who said that they were willing to share personal
information with retailers in order to receive personalized offers from retailers were 55%, 46% and
72%, respectively. Suppose you randomly select 5 consumers from each of the three countries.
-Referring to Scenario 5-7, the probability that at least 3 consumers from China are willing to
share personal information with retailers in order to receive personalized offers from retailers is
________.

Accepted Answer

The answer of SCENARIO 5-7
A consulting firm that surveyed consumers'...

Question 17

The diameters of 10 randomly selected bolts have a binomial distribution.

Accepted Answer

A) True 
 B)False

Question 18

SCENARIO 5-7
A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of
consumers from the U.S., Canada, and China who said that they planned to spend more on holiday
shopping were 40%, 34% and 73%, respectively. The survey also found that the percentage of
consumers from the U.S., Canada, and China who said that they were willing to share personal
information with retailers in order to receive personalized offers from retailers were 55%, 46% and
72%, respectively. Suppose you randomly select 5 consumers from each of the three countries.
-Referring to Scenario 5-7, the probability that all 5 consumers from China plan to spend more
on holiday shopping is ________.

Accepted Answer

The answer of SCENARIO 5-7
A consulting firm that surveyed consumers'...

Question 19

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 6.4 tickets per day. Find the probability that less than 6 tickets are written on a
randomly selected day from this population.

Accepted Answer

The answer of The local police department must write, on...

Question 20

The Department of Commerce in a particular state has determined that the number of small
businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean
of 6.4. Find the probability that more than 3 bankruptcies occur next month.

Accepted Answer

The answer of The Department of Commerce in a particular...

Exam 5: Discrete Probability Distributions

Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

If the outcomes of a variable follow a Poisson distribution, then their

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.

If π remains constant in a binomial distribution, an increase in n will increase the variance.

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 standard deviation of the number of times she will be audited is ________.

If n = 10 and π = 0.70, then the mean of the binomial distribution is

A probability distribution is an equation that

If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .

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.

The diameters of 10 randomly selected bolts have a binomial distribution.

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that more than 3 bankruptcies occur next month.