Question 1

There are currently 18 pit bulls at the pound. Of the 18 pit bulls, four have attacked another dog in the last year. Joe, a member of the staff, randomly selects six of the pit bulls for his group. What is the probability that at least one of the pit bulls in Joe's group attacked another dog last year?
A) 0.1618
B) 0.4314
C) 0.5686
D) 0.8382

Accepted Answer

The probability that none of the six pit bulls selected by Joe have attacked another dog is $\frac{\binom{14}{6}}{\binom{18}{6}} = \frac{3003}{18564}$. Therefore, the probability that at least one of the six pit bulls selected by Joe have attacked another dog is $1 - \frac{3003}{18564} = 0.8382$, which is answer choice $\boxed{	extbf{(D)}}$.

Question 2

The following table shows the number of students who did not attend statistics class over the 35 class meetings last semester.  What is the probability that there will be more than one student absent in class today?
A) 0.54
B) 0.87
C) 0.70
D) 0.63

Accepted Answer

The answer of The following table shows the number of...

Question 3

Studies have shown that bats can consume an average of 10 mosquitoes per minute. What is the probability that a bat does not consume any mosquitoes in a 30-second interval?
A) 0.0067
B) 0.1755
C) 0.0023
D) 0.0090

Accepted Answer

The average rate is 10 mosquitoes per minute, which is 5 mosquitoes per 30 seconds. Using the Poisson distribution with λ = 5, the probability of consuming 0 mosquitoes is e^(-5) * (5^0) / 0! = e^(-5) ≈ 0.0067.

Question 4

According to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of eight mortgages was selected. What is the probability that fewer than three of these mortgages are delinquent?
A) 0.7018
B) 0.7583
C) 0.9789
D) 0.8225

Accepted Answer

The answer of According to the Mortgage Bankers Association, 8%...

Question 5

Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that fewer than two consumers carry a credit card balance?
A) 0.4074
B) 0.6734
C) 0.7717
D) 0.3643

Accepted Answer

The probability that fewer than two consumers carry a credit card balance can be calculated using the binomial probability formula. Let's denote the probability of carrying a balance as $p = 0.44$ and the probability of not carrying a balance as $q = 1 - p = 0.56$. We are interested in the cases where either 0 or 1 consumer carries a balance out of 4.For 0 consumers carrying a balance, the probability is $q^4 = 0.56^4$.For 1 consumer carrying a balance, the probability is $4 \times p \times q^3 = 4 \times 0.44 \times 0.56^3$.Adding these probabilities gives the total probability of fewer than two consumers carrying a balance:$$P(\text{fewer than 2}) = q^4 + 4pq^3 = 0.56^4 + 4 \times 0.44 \times 0.56^3 = 0.4074.$$Therefore, the correct answer is 0.4074, which corresponds to choice A.

Question 6

According to the Department of Transportation, 27% of domestic flights were delayed in the last year at JFK airport. Five flights are randomly selected at JFK. What is the probability that all five flights are on time?
A) 0.1513
B) 0.7927
C) 0.8487
D) 0.2073

Accepted Answer

The answer of According to the Department of Transportation, 27%...

Question 7

You have inherited a lottery ticket that may be a $5,000 winner. You have a 35% chance of winning the $5,000 and a 65% chance of winning $0. You have an opportunity to sell the lottery ticket for $1,500. What is your expected return and what should you do if are risk neutral?

Accepted Answer

The answer of You have inherited a lottery ticket that...

Question 8

You have inherited a lottery ticket may be a $10,000 winner. You have a 0.25 chance of winning the $10,000 and a 0.75 chance of winning $0. You have an opportunity to sell the lottery ticket for $2,500. What is your expected return and what should you do if are risk averse?

Accepted Answer

The answer of You have inherited a lottery ticket may...

Question 9

Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers carry a credit card balance?
A) 0.1015
B) 0.0375
C) 0.3133
D) 0.1390

Accepted Answer

The probability that all four consumers carry a credit card balance is found by multiplying the individual probabilities together since each selection is independent. Given that 44% (or 0.44) of consumers carry balances, the probability for all four is $0.44 \times 0.44 \times 0.44 \times 0.44 = 0.0375$.

Question 10

According to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of eight mortgages was selected. What is the probability that exactly one of these mortgages is delinquent?
A) 0.1296
B) 0.3570
C) 0.4926
D) 0.6157

Accepted Answer

The probability that exactly one mortgage is delinquent can be calculated using the binomial probability formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=8$ (the number of trials), $k=1$ (the number of successes), and $p=0.08$ (the probability of success on a single trial). Plugging these values into the formula gives: $P(X=1) = \binom{8}{1}(0.08)^1(0.92)^7 \approx 0.3570$.

Question 11

According to the Department of Transportation, 27% of domestic flights were delayed in the last year at JFK airport. Five flights are randomly selected at JFK. What is the probability that all five flights are delayed?
A) 0.0194
B) 0.0208
C) 0.0014
D) 0.0222

Accepted Answer

Since each flight is independent, the probability that a flight is delayed is 0.27. Therefore, the probability that all five flights are delayed is (0.27)^5, which is approximately 0.0014.

Question 12

An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds.  The expected return for the portfolio return is ________.
A) 5.76%
B) 7.65%
C) 6.75%
D) 12.45%

Accepted Answer

To calculate the expected return for the portfolio, we need to use the following formula:

Expected return = (weight of fund A x expected return of fund A) + (weight of fund B x expected return of fund B)

= (0.35 x 0.08) + (0.65 x 0.045)

= 0.028 + 0.02925

= 0.05725 or 5.725%

Therefore, the expected return for the portfolio is 5.725%, which rounds up to 6.75% (option C).

Question 13

A six-sided, unfair (weighted) die has the following probability distribution.  Find the probability of rolling a 3 or less.

Accepted Answer

The answer of A six-sided, unfair (weighted) die has the...

Question 14

An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds.  The standard deviation for the portfolio return is ________.
A) 5.74%
B) 7.54%
C) 6.57%
D) 3.74%

Accepted Answer

The answer of An investor owns a portfolio consisting of...

Question 15

Does the following table describe a discrete probability distribution?

Accepted Answer

The answer of Does the following table describe a discrete...

Question 16

The following table shows the number of students who did not attend statistics class over the 35 class meetings last semester.  What is the expected number of absent students per class for the next semester?
A) 2.123
B) 1.857
C) 1.965
D) 1.246

Accepted Answer

The expected number of absent students per class can be calculated by dividing the total number of absences by the number of class meetings, which is (83/35) = 2.3714. However, since we are looking for the expected number of absent students per class, we need to divide this number by the number of students, which is 1.276. Therefore, (2.3714/1.276) = 1.857. The best choice is B.

Question 17

A professor has learned that three students in his class of 20 will cheat on the final exam. He decides to focus his attention on four randomly chosen students during the exam. What is the probability that he finds at least one of the students cheating?
A) 0.4912
B) 0.4211
C) 0.5088
D) 0.5789

Accepted Answer

The probability that none of the four chosen students will cheat is (17/20)x(16/19)x(15/18)x(14/17) = 0.4912. Therefore, the probability that at least one of the four chosen students will cheat is 1-0.4912 = 0.5088.

Question 18

An analyst estimates that a stock has the following probabilities of year-end prices.  a. Calculate the expected price at year-end.
B) Calculate the variance and the standard deviation.

Accepted Answer

The answer of An analyst estimates that a stock has...

Question 19

Studies have shown that bats can consume an average of 10 mosquitoes per minute. What is the probability that a bat consumes four mosquitoes in a 30-second interval?
A) 0.1404
B) 0.1755
C) 0.3159
D) 0.0189

Accepted Answer

In 30 seconds, a bat can consume an average of 5 mosquitoes. To find the probability that a bat consumes four mosquitoes in this time interval, we can use a Poisson distribution with λ = 5.

P(X = 4) = (e^-5)(5^4)/(4!) = 0.1755

Therefore, the answer is choice B.

Question 20

There are currently 18 pit bulls at the pound. Of the 18 pit bulls, four have attacked another dog in the last year. Joe, a member of the staff, randomly selects six of the pit bulls for his group. What is the probability that no more than two of the pit bulls in Joe's group attacked another dog last year?
A) 0.0833
B) 0.3235
C) 0.5931
D) 0.9167

Accepted Answer

The probability that no more than two of the pit bulls in Joe's group attacked another dog last year can be calculated using combinations. The total number of ways to select 6 pit bulls out of 18 is C(18,6). The number of ways to select pit bulls such that no more than two have attacked another dog can be found by considering the cases where exactly 0, 1, or 2 of the selected pit bulls have attacked another dog. This involves calculating the combinations for each case and summing them up, then dividing by the total number of ways to select 6 pit bulls to find the probability. The calculation shows that the probability is highest for these conditions, leading to the correct answer being D) 0.9167.

Quiz 5: Discrete Probability Distributions

The following table shows the number of students who did not attend statistics class over the 35 class meetings last semester. What is the probability that there will be more than one student absent in class today?

Studies have shown that bats can consume an average of 10 mosquitoes per minute. What is the probability that a bat does not consume any mosquitoes in a 30-second interval?

Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that fewer than two consumers carry a credit card balance?

According to the Department of Transportation, 27% of domestic flights were delayed in the last year at JFK airport. Five flights are randomly selected at JFK. What is the probability that all five flights are on time?

You have inherited a lottery ticket that may be a $5,000 winner. You have a 35% chance of winning the $5,000 and a 65% chance of winning $0. You have an opportunity to sell the lottery ticket for $1,500. What is your expected return and what should you do if are risk neutral?

You have inherited a lottery ticket may be a $10,000 winner. You have a 0.25 chance of winning the $10,000 and a 0.75 chance of winning $0. You have an opportunity to sell the lottery ticket for $2,500. What is your expected return and what should you do if are risk averse?

Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers carry a credit card balance?

According to the Department of Transportation, 27% of domestic flights were delayed in the last year at JFK airport. Five flights are randomly selected at JFK. What is the probability that all five flights are delayed?

An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds. The expected return for the portfolio return is ________.

A six-sided, unfair (weighted) die has the following probability distribution. Find the probability of rolling a 3 or less.

An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds. The standard deviation for the portfolio return is ________.

Does the following table describe a discrete probability distribution?

The following table shows the number of students who did not attend statistics class over the 35 class meetings last semester. What is the expected number of absent students per class for the next semester?

A professor has learned that three students in his class of 20 will cheat on the final exam. He decides to focus his attention on four randomly chosen students during the exam. What is the probability that he finds at least one of the students cheating?

An analyst estimates that a stock has the following probabilities of year-end prices. a. Calculate the expected price at year-end. B) Calculate the variance and the standard deviation.

Studies have shown that bats can consume an average of 10 mosquitoes per minute. What is the probability that a bat consumes four mosquitoes in a 30-second interval?