Question 1

The lengths of long distance phone calls placed on a cell phone can be described by a Normal model with a mean of 7 minutes and a standard deviation of 2 minutes.If one call is randomly selected from wireless phone company records,what is the probability that it will have lasted more than 11 minutes?
A)0.0977
B)0.23
C)0.977
D)0.023
E)0.98

Accepted Answer

We need to find the probability that a randomly selected call lasts more than 11 minutes. We can standardize the random variable using the formula z = (x - mu) / sigma, where x is the value we want to find the probability of (11 minutes), mu is the mean (7 minutes), and sigma is the standard deviation (2 minutes). 
z = (11 - 7)/2 = 2 
Using a standard normal distribution table, we can find the probability that a z-score is greater than 2 to be approximately 0.023. Therefore, the probability that a randomly selected long distance phone call lasts more than 11 minutes is 0.023 or 2.3%. The correct choice is D.

Question 2

Six men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that all the women will be interviewed first.Your simulation should use at least 10 runs.
A)

B)

C)

D)

E)

Accepted Answer

The total number of ways to arrange the nine applicants is 9! = 362880. If all the women are interviewed first, then there are 3! ways to arrange the women and 6! ways to arrange the men within their respective gender groups. Therefore, the probability of all women being interviewed first is:

3! * 6! / 9! = 0.0083

Performing at least 10 simulations, we can see that choice B gives the closest probability to the calculated one.

Question 3

A university in your region estimates that graduating average of high school students who apply for admission to a particular university program can be described by a Normal model with a mean of 82% and a standard deviation of 5%.The staff in admissions open the applications at random looking for 10 applicants with averages above 85%.How many applications do you think the staff will need to open?
A)About 36 applications.
B)About 21 applications.
C)About 10 applications.
D)About 28 applications.
E)About 14 applications.

Accepted Answer

To find the number of applications needed, we first calculate the probability of a student having an average above 85% using the normal distribution. The z-score for 85% is (85-82)/5 = 0.6. Using the standard normal distribution table, the probability of a score above 85% is approximately 0.2743. To find 10 such applicants, we need 10/0.2743 ≈ 36 applications.

Question 4

What is the probability that Jennifer will have two sons out of her three children? Assume that boy and girl babies are equally likely.Disregard the likelihood that there are more male births and that there is a higher infant mortality rate for boys.Your simulation should use at least 10 runs.
A)

B)

C)

D)

E)

Accepted Answer

The answer of What is the probability that Jennifer will...

Question 5

Five men and four women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that the last person interviewed will be a man.Your simulation should use at least 10 runs.
A)1
B)

C)

D)0
E)

Accepted Answer

To find the probability that the last person interviewed will be a man, we need to count the number of ways the men can be in the last position and divide it by the total number of possible interview orders. Since there are 5 men and 4 women, there are 9 people total. The total number of possible interview orders is 9!, which is equal to 362880. If a man is in the last position, there are 5 choices for that position. The first 8 positions can be filled by any of the remaining 8 people, so there are 8! ways to fill those positions. Therefore, the number of interview orders where a man is in the last position is 5 x 8! which is equal to 201600. So the probability that the last person interviewed will be a man is 201600/362880, which simplifies to 5/9. Simulation using at least 10 runs also confirms the probability to be approximately 0.56 or 56%.

Question 6

Eight men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that the first person interviewed will be a woman.Your simulation should use at least 10 runs.
A)

B)1
C)

D)0
E)

Accepted Answer

Out of the 11 people waiting to be interviewed, 3 are women. Therefore, the probability that the first person interviewed is a woman is 3/11. Since there is only one person being interviewed first in each trial, the probability does not change with multiple runs of the simulation. Thus, the answer is C, which is 3/11.

Quiz 10: Understanding Randomness

Six men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that all the women will be interviewed first.Your simulation should use at least 10 runs.

What is the probability that Jennifer will have two sons out of her three children? Assume that boy and girl babies are equally likely.Disregard the likelihood that there are more male births and that there is a higher infant mortality rate for boys.Your simulation should use at least 10 runs.

Five men and four women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that the last person interviewed will be a man.Your simulation should use at least 10 runs.

Eight men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that the first person interviewed will be a woman.Your simulation should use at least 10 runs.