Deck 27: Modeling With Probability

Question 1

In a particular production process, drying times for newly pained parts are
Uniformly distributed between 2 and 8 minutes. The probability that a part dries in less
Than 6 minutes is

A) 2 / 6
B) 2 / 8
C) 3 / 6
D) 4 / 6
E) 4 / 8

Answer 1

D

Question 2

IT staff for a large corporation has developed the following probability
Distribution for the number of calls requiring troubleshooting problems per day. Based
On the distribution, the expected number of calls per day is $\begin{array}{cc}\text { Number of Calls } & \text { Probability } \\0 & .32 \\1 & .35 \\2 & .18 \\3 & .10 \\4 & .05\end{array}$

A) 2.77
B) 1.56
C) 1.21
D) 1.31
E) 1

Answer 2

1.21

Question 3

Suppose the time it takes for a purchasing agent to complete an online ordering
Process is normally distributed with a mean of 8 minutes and a standard deviation of 2
Minutes. Suppose a random sample of 25 ordering processes is selected. What is the
Probability that the sample mean will be less than 7.5 minutes?

A) .3944
B) .1056
C) .2114
D) .4013
E) .8944

Answer 3

B

Question 4

As a result of the financial crisis on Wall Street in September 2008 that required
Federal government intervention, a survey showed that 40% of Americans reallocated
Their investments to reduce exposure to the stock market. What is the probability that out
Of 5 randomly selected Americans, none will have reallocated their investments in this
Way?

A) .2592
B) .8154
C) .1699
D) .0778
E) .1234

Question 5

Suppose the time it takes for a purchasing agent to complete an online ordering
Process is normally distributed with a mean of 8 minutes and a standard deviation of 2
Minutes. What is the probability that it takes longer than 11 minutes for the purchasing
Agent to complete the process?

A) 0.9332
B) 0.4332
C) 0.0668
D) 0.5668
E) none of the above

Question 6

A government agency has 6000 employees. As an alternative to the traditional
Five day work week, employees were asked whether they preferred a four day work week
(10 hours per day) or flexible hours. The table below shows the results by age category.
Which of the following statements is true about work week preferences and age
Category? $$\begin{array} { | l | l | l | } \hline \text { Age Category } & \begin{array} { l } \text { Prefers 4 } \\\text { Day Week }\end{array} & \begin{array} { l } \text { Prefers Flex } \\\text { Hours }\end{array} \\\hline \text { Under 30 } & 600 & 300 \\\hline 30 - 45 & 1200 & 1500 \\\hline \text { Over 45 } & 2100 & 300 \\\hline\end{array}$$

A) Work week preferences are independent of age category.
B) Work week preferences are mutually exclusive.
C) Work week preferences are not independent of age category.
D) Work week preferences are independent and mutually exclusive.
E) There is insufficient information to determine whether work week preferences and

Question 7

A men's clothing store has determined the following probability distribution for
The number of special size orders placed per month. Based on this distribution, the
Standard deviation in the number of special size orders placed per month is $\begin{array}{cc}\text { Number Ordered } & \text { Probability } \\0 & .10 \\5 & .10 \\10 & .12 \\15 & .30 \\20 & .38\end{array}$

A) 43.56
B) 6.6
C) 15.345
D) 4.9
E) 3.88

Question 8

A telecommunications company is interested in determining the likelihood of a
New breakthrough technology being developed in the next ten years. What type of
Probability would they estimate?

A) Relative Frequency
B) Classical
C) Personal
D) Mathematical
E) Empirical

Question 9

The number of claims for lost luggage in a small city airport averages nine per
Day) Assuming the Poisson distribution, what is the probability that there will be fewer
Than 3 claims on any given day?

A) .0150
B) .0212
C) .0062
D) .0337
E) .5000

Question 10

A quality assurance manager is interested in determining the likelihood that more
Than 20 calls come in to a particular customer service center per hour. What method
Would be most appropriate for assigning this probability?

A) Personal
B) Judgmental
C) Subjective
D) Relative Frequency
E) Classical

Question 11

A publishing company conducted a survey of its readership and found that 60%
Subscribed to Food & Wine, 30% subscribed to Wine Spectator, and 25% subscribed to
Both. The probability that a reader does not subscribe to either is

A) .10
B) .65
C) .50
D) .45
E) .35

Question 12

A survey of investors finds that 60% use a full service brokerage firm to invest in
Stocks, 30% trade stocks online and 24% do both. The probability that an investor
Selected at random uses a full service brokerage firm or trades stocks online is

A) 90%
B) 66%
C) 34%
D) 54%
E) 60%

Question 13

An advocacy group is investigating whether gender has an effect on job category
In large investment firms. Given the results shown in the table below, which of the
Following statements is true about gender and job category? $$\begin{array} { | l | l | l | } \hline \text { Job Category } & \text { Male } & \text { Female } \\\hline \text { Clerical / Technical } & 85 & 215 \\\hline \text { Professional Staff } & 720 & 480 \\\hline \text { Executive / Managerial } & 400 & 100 \\\hline\end{array}$$

A) Gender and job category are independent.
B) Gender and job category are not independent.
C) Gender and job category are mutually exclusive.
D) Gender and job category are independent and mutually exclusive.
E) There is not sufficient information to determine whether gender and job category

Question 14

Suppose the time it takes for a purchasing agent to complete an online ordering
Process is normally distributed with a mean of 8 minutes and a standard deviation of 2
Minutes. Suppose a random sample of 25 ordering processes is selected. The standard
Deviation of the sampling distribution of mean times is

A) 0.4 minutes
B) 2 minutes
C) 0.08 minutes
D) 1.6 minutes
E) 0.12 minutes

Question 15

Insurance company records indicate that 10% of its policyholders file claims
Involving theft or robbery of personal property from their homes. Suppose a random
Sample of 400 policyholders is selected. The standard deviation of the sampling
Distribution of the sample proportion of policyholders filing claims involving theft or
Robbery from their homes is

A) .000225
B) 0.25
C) .0455
D) .1667
E) .015

Question 16

IT staff for a large corporation has developed the following probability
Distribution for the number of calls requiring troubleshooting problems per day. Based
On the distribution, the standard deviation in the number of calls per day is $\begin{array}{cc}\text { Number of Calls } & \text { Probability } \\0 & .32 \\1 & .35 \\2 & .18 \\3 & .10 \\4 & .05\end{array}$

A) 1.31
B) 1.14
C) 2.77
D) 1.56
E) 1.21

Question 17

Insurance company records indicate that 10% of its policyholders file claims
Involving theft or robbery of personal property from their homes. Suppose a random
Sample of 400 policyholders is selected. The probability that the sample proportion of
Policyholders filing claims involving theft or robbery from their homes is less than 8% is

A) .0918
B) .1333
C) .4082
D) .0517
E) .7892

Question 18

A theorem that allows us to use the normal probability distribution to approximate
The sampling distribution of the sample mean whenever the sample size is large (over 30)
Is the

A) approximation theorem
B) central normality theorem
C) central limit theorem
D) normal probability theorem
E) normal sampling theorem

Question 19

An advocacy group is investigating whether gender has an effect on job category
In large investment firms. She surveyed a sample of firms with the following results: $$\begin{array} { | l | l | l | } \hline \text { Job Category } & \text { Male } & \text { Female } \\\hline \text { Clerical / Technical } & 85 & 215 \\\hline \text { Professional Staff } & 720 & 480 \\\hline \text { Executive / Managerial } & 400 & 100 \\\hline\end{array}$$
What is the probability that a randomly selected employee's job category is executive /
Managerial given that she is female?

A) .13
B) .20
C) .80
D) .05
E) .45

Question 20

A government agency has 6000 employees. As an alternative to the traditional
Five day work week, employees were asked whether they preferred a four day work week
(10 hours per day) or flexible hours. The table below shows the results by age category.
What is the probability that an employee at this government agency prefers a four day
Work week? $$\begin{array} { | l | l | l | } \hline \text { Age Category } & \begin{array} { l } \text { Prefers 4 } \\\text { Day Week }\end{array} & \begin{array} { l } \text { Prefers Flex } \\\text { Hours }\end{array} \\\hline \text { Under } 30 & 600 & 300 \\\hline 30 - 45 & 1200 & 1500 \\\hline \text { Over 45 } & 2100 & 300 \\\hline\end{array}$$

A) .54
B) .15
C) .50
D) .35
E) .65