Question 1

The amount of time between successive TV watching by first graders follows an exponential
distribution with a mean of 10 hours. The probability that a given first grader spends more than 5
hours between successive TV watching is ______.

Accepted Answer

The answer of The amount of time between successive TV...

Question 2

A company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting
Time was found to be a variable best approximated by an exponential distribution with a mean
Length of waiting time equal to 3 minutes (i.e. the mean number of calls answered in a minute is
1/3). What proportion of customers having to hold more than 1.5 minutes will hang up before
Placing an order?
A) 0.86466
B) 0.60653
C) 0.39347
D) 0.13534

Accepted Answer

The answer of A company that receives the majority of...

Question 3

SCENARIO 5-14
An accounting firm in a college town usually recruits employees from two of the universities in town.
This year, there are fifteen graduates from University A and five from University B and the firm
decides to hire six new employees from the two universities.
-Referring to Scenario 5-14, what is the probability that at least one of the new employees will be
from University A?

Accepted Answer

The answer of SCENARIO 5-14
An accounting firm in a college...

Question 4

Let X represent the amount of time till the next student will arrive in the library parking lot at the university. If we know that the distribution of arrival time can be modeled using an exponential
Distribution with a mean of 4 minutes (i.e. the mean number of arrivals is 1/4 per minute), find
The probability that it will take between 2 and 12 minutes for the next student to arrive at the
Library parking lot.
A) 0.049787
B) 0.556744
C) 0.606531
D) 0.656318

Accepted Answer

The answer of Let X represent the amount of time...

Question 5

Let X represent the amount of time until the next student will arrive in the library parking lot at the university. If we know that the distribution of arrival time can be modeled using an
Exponential distribution with a mean of 4 minutes (i.e. the mean number of arrivals is 1/4 per
Minute), find the probability that it will take more than 10 minutes for the next student to arrive at
The library parking lot.
A) 0.917915
B) 0.670320
C) 0.329680
D) 0.082085

Accepted Answer

The probability that it will take more than 10 minutes for the next student to arrive is given by the survival function of the exponential distribution: P(X > 10) = exp(-10/4) = exp(-2.5) ≈ 0.082085.

Question 6

SCENARIO 5-14
An accounting firm in a college town usually recruits employees from two of the universities in town.
This year, there are fifteen graduates from University A and five from University B and the firm
decides to hire six new employees from the two universities.
-Referring to Scenario 5-14, what is the probability that at least two of the new employees will be
from University B?

Accepted Answer

The answer of SCENARIO 5-14
An accounting firm in a college...

Question 7

SCENARIO 5-14
An accounting firm in a college town usually recruits employees from two of the universities in town.
This year, there are fifteen graduates from University A and five from University B and the firm
decides to hire six new employees from the two universities.
-Referring to Scenario 5-14, what is the probability that no more than four of the new employees
will be from University A?

Accepted Answer

The answer of SCENARIO 5-14
An accounting firm in a college...

Question 8

The interval between patients arriving at an outpatient clinic follows an exponential distribution
with mean 15 minutes. What is the probability that a randomly chosen arrival to be less than 15
minutes?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 9

SCENARIO 5-14
An accounting firm in a college town usually recruits employees from two of the universities in town.
This year, there are fifteen graduates from University A and five from University B and the firm
decides to hire six new employees from the two universities.
-Referring to Scenario 5-14, what is the probability that all of the new employees will be from
University B?

Accepted Answer

The answer of SCENARIO 5-14
An accounting firm in a college...

Question 10

SCENARIO 5-14
An accounting firm in a college town usually recruits employees from two of the universities in town.
This year, there are fifteen graduates from University A and five from University B and the firm
decides to hire six new employees from the two universities.
-Referring to Scenario 5-14, what is the probability that more than four of the new employees will
be from University A?

Accepted Answer

The answer of SCENARIO 5-14
An accounting firm in a college...

Question 11

A company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting
Time was found to be a variable best approximated by an exponential distribution with a mean
Length of waiting time equal to 2.8 minutes (i.e. the mean number of calls answered in a minute is
1/2)8). What is the probability that a randomly selected caller is placed on hold fewer than 7
Minutes?
A) 0.0009119
B) 0.082085
C) 0.917915
D) 0.9990881

Accepted Answer

The exponential distribution with a mean of 2.8 minutes has a rate parameter λ = 1/2.8. The probability that a caller waits less than 7 minutes is given by the cumulative distribution function: P(X < 7) = 1 - e^(-λ*7). Calculating this gives approximately 0.917915.

Question 12

The amount of time between successive TV watching by first graders follows an exponential
distribution with a mean of 10 hours. The probability that a given first grader spends between 10
and 15 hours between successive TV watching is ______.

Accepted Answer

The answer of The amount of time between successive TV...

Question 13

The amount of time between successive TV watching by first graders follows an exponential
distribution with a mean of 10 hours. The probability that a given first grader spends less than 20
hours between successive TV watching is ______.

Accepted Answer

The answer of The amount of time between successive TV...

Question 14

The interval between patients arriving at an outpatient clinic follows an exponential distribution
with mean 15 minutes. What is the probability that a randomly chosen arrival to be more than 18
minutes?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 15

The interval between patients arriving at an outpatient clinic follows an exponential distribution
at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be
less than 15 minutes?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 16

A company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting
Time was found to be a variable best approximated by an exponential distribution with a mean
Length of waiting time equal to 2.8 minutes (i.e. the mean number of calls answered in a minute is
1/2)8). What proportion of callers is put on hold longer than 2.8 minutes?
A) 0.3679
B) 0.50
C) 0.60810
D) 0.6321

Accepted Answer

The proportion of callers put on hold longer than 2.8 minutes is given by the cumulative distribution function of the exponential distribution, which is given by 1 - e^(-x/mean). In this case, the mean is 2.8 minutes, so the proportion of callers put on hold longer than 2.8 minutes is 1 - e^(-2.8/2.8) = 0.3679.

Question 17

The interval between patients arriving at an outpatient clinic follows an exponential distribution
with mean 15 minutes. What is the mean number of arrivals per minute?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 18

A company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting
Time was found to be a variable best approximated by an exponential distribution with a mean
Length of waiting time equal to 3 minutes (i.e. the mean number of calls answered in a minute is
1/3). Find the waiting time at which only 10% of the customers will continue to hold.
A) 2.3 minutes
B) 3.3 minutes
C) 6.9 minutes
D) 13.8 minutes

Accepted Answer

The exponential distribution's cumulative distribution function (CDF) is used to find the waiting time. For 10% of customers to continue holding, we solve for t in 1 - e^(-t/3) = 0.10, which gives t ≈ 6.9 minutes.

Question 19

A company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting
Time was found to be a variable best approximated by an exponential distribution with a mean
Length of waiting time equal to 3 minutes (i.e. the mean number of calls answered in a minute is
1/3). What proportion of customers having to hold more than 4.5 minutes will hang up before
Placing an order?
A) 0.22313
B) 0.48658
C) 0.51342
D) 0.77687

Accepted Answer

The proportion of customers having to hold more than 4.5 minutes is given by the cumulative distribution function of the exponential distribution with mean 3 minutes, evaluated at 4.5 minutes. This is equal to 1 - exp(-4.5/3) = 0.22313.

Question 20

SCENARIO 5-14
An accounting firm in a college town usually recruits employees from two of the universities in town.
This year, there are fifteen graduates from University A and five from University B and the firm
decides to hire six new employees from the two universities.
-Referring to Scenario 5-14, what is the probability that no more than two of the new employees
will be from University B?

Accepted Answer

The answer of SCENARIO 5-14
An accounting firm in a college...

Quiz 20: Probability and Combinatorics

The amount of time between successive TV watching by first graders follows an exponential distribution with a mean of 10 hours. The probability that a given first grader spends more than 5 hours between successive TV watching is ______.

The interval between patients arriving at an outpatient clinic follows an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be less than 15 minutes?

The amount of time between successive TV watching by first graders follows an exponential distribution with a mean of 10 hours. The probability that a given first grader spends between 10 and 15 hours between successive TV watching is ______.

The amount of time between successive TV watching by first graders follows an exponential distribution with a mean of 10 hours. The probability that a given first grader spends less than 20 hours between successive TV watching is ______.

The interval between patients arriving at an outpatient clinic follows an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be more than 18 minutes?

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be less than 15 minutes?

The interval between patients arriving at an outpatient clinic follows an exponential distribution with mean 15 minutes. What is the mean number of arrivals per minute?