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

Accepted Answer

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 $\begin{array}{cc}
\text { Number of Calls } & \text { Probability } \
0 & .32 \
1 & .35 \
2 & .18 \
3 & .10 \
4 & .05
\end{array}$

Accepted Answer

C

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?

Accepted Answer

The standard error of the mean is 2/sqrt(25) = 0.4. The z-score for 7.5 is (7.5-8)/0.4 = -1.25. Using the standard normal distribution table, the probability of a z-score being less than -1.25 is approximately 0.1056.

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?

Accepted Answer

The answer of As a result of the financial crisis...

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?

Accepted Answer

The Z-score for 11 minutes is (11-8)/2 = 1.5. The probability of a Z-score greater than 1.5 is 0.0668.

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? $$\begin{array} { | l | l | l | } 
\hline \text { Age Category } & \begin{array} { l } 
\text { Prefers 4 } \
\text { Day Week }
\end{array} & \begin{array} { l } 
\text { Prefers Flex } \
\text { Hours }
\end{array} \
\hline \text { Under 30 } & 600 & 300 \
\hline 30 - 45 & 1200 & 1500 \
\hline \text { Over 45 } & 2100 & 300 \
\hline
\end{array}$$

Accepted Answer

The distribution of preferences varies significantly across age categories, indicating that work week preferences are not independent of age category.

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 $\begin{array}{cc}
\text { Number Ordered } & \text { Probability } \
0 & .10 \
5 & .10 \
10 & .12 \
15 & .30 \
20 & .38
\end{array}$

Accepted Answer

The answer of A men's clothing store has determined the...

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?

Accepted Answer

Personal probability is used when estimating the likelihood of an event based on subjective judgment or opinion, such as predicting future technological breakthroughs.

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?

Accepted Answer

The answer of The number of claims for lost luggage...

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?

Accepted Answer

Relative frequency is appropriate as it involves using historical data to estimate the probability of an event occurring.

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

Accepted Answer

Using the principle of inclusion-exclusion, the probability that a reader subscribes to at least one magazine is 0.60 + 0.30 - 0.25 = 0.65. Therefore, the probability that a reader does not subscribe to either is 1 - 0.65 = 0.35.

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

Accepted Answer

The probability that an investor uses a full service brokerage firm or trades stocks online is calculated using the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B). Here, P(A) = 60%, P(B) = 30%, and P(A and B) = 24%. So, P(A or B) = 60% + 30% - 24% = 66%.

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? $$\begin{array} { | l | l | l | } 
\hline \text { Job Category } & \text { Male } & \text { Female } \
\hline \text { Clerical / Technical } & 85 & 215 \
\hline \text { Professional Staff } & 720 & 480 \
\hline \text { Executive / Managerial } & 400 & 100 \
\hline
\end{array}$$

Accepted Answer

The distribution of males and females across job categories is not proportional, indicating a potential dependence between 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

Accepted Answer

The standard deviation of the sampling distribution (standard error) is calculated as the population standard deviation divided by the square root of the sample size: 2 / √25 = 0.4 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

Accepted Answer

The standard deviation of the sampling distribution of the sample proportion is calculated using the formula: sqrt[(p(1-p))/n], where p is the population proportion (0.10) and n is the sample size (400). This gives sqrt[(0.10*0.90)/400] = 0.015.

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 $\begin{array}{cc}
\text { Number of Calls } & \text { Probability } \
0 & .32 \
1 & .35 \
2 & .18 \
3 & .10 \
4 & .05
\end{array}$

Accepted Answer

To find the standard deviation, first calculate the expected value (mean) of the distribution, then use it to find the variance, and finally take the square root of the variance. The calculations lead to a standard deviation of approximately 1.14.

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

Accepted Answer

The sample proportion follows a normal distribution with mean 0.10 and standard deviation sqrt((0.10*0.90)/400). Using the z-score formula, we find the probability that the sample proportion is less than 0.08, which corresponds to a z-score of approximately -1.34. The probability of a z-score less than -1.34 is approximately 0.0918.

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

Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will approximate a normal distribution as the sample size becomes large, typically over 30.

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?

Accepted Answer

The answer of An advocacy group is investigating whether gender...

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? $$\begin{array} { | l | l | l | } 
\hline \text { Age Category } & \begin{array} { l } 
\text { Prefers 4 } \
\text { Day Week }
\end{array} & \begin{array} { l } 
\text { Prefers Flex } \
\text { Hours }
\end{array} \
\hline \text { Under } 30 & 600 & 300 \
\hline 30 - 45 & 1200 & 1500 \
\hline \text { Over 45 } & 2100 & 300 \
\hline
\end{array}$$

Accepted Answer

The answer of A government agency has 6000 employees. As...

Quiz 27: Modeling With Probability

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

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 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?

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 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 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 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 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