Question 1

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR).In 180 days of school,about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
A)5 days
B)45 days
C)65 days
D)81 days

Accepted Answer

The proportion of teachers certified in CPR is 36 out of 80, which simplifies to 9 out of 20. To find out how many days out of 180 a CPR-certified teacher would likely be on bus duty, multiply the total days by this proportion: $180 \times \frac{9}{20} = 81$ days.

Question 2

A probability distribution is an equation that
A)associates a particular probability of occurrence with each outcome.
B)measures outcomes and assigns values of X to the simple events.
C)assigns a value to the variability of the set of events.
D)assigns a value to the center of the set of events.

Accepted Answer

A probability distribution assigns a particular probability of occurrence with each outcome. It provides a way of quantifying the likelihood of different outcomes of a random variable.

Question 3

A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.025.To find the probability that exactly 20 of the computers will require repair on a given day,one will use what type of probability distribution?
A)Binomial distribution
B)Poisson distribution
C)Hypergeometric distribution
D)None of the above

Accepted Answer

The situation described fits the conditions for a binomial distribution: 
- There are a fixed number of trials (125 computers)
- Each trial has two possible outcomes (require repair or do not require repair)
- The probability of success (requiring repair) is constant from trial to trial (0.025)
- The trials are independent of each other.

Question 4

A stock analyst was provided with a list of 25 stocks.He was expected to pick 3 stocks from the list whose prices are expected to rise by more than 20% after 30 days.In reality,the prices of only 5 stocks would rise by more than 20% after 30 days.If he randomly selected 3 stocks from the list,he would use what type of probability distribution to compute the probability that all of the chosen stocks would appreciate more than 20% after 30 days?
A)Binomial distribution
B)Poisson distribution
C)Hypergeometric distribution
D)None of the above

Accepted Answer

The scenario described fits the hypergeometric distribution because we are selecting a specific number of items (3 stocks) from a finite population (25 stocks), without replacement, and we are interested in the number of successes (stocks whose prices rise by more than 20%). The binomial distribution assumes independent trials with a fixed probability of success, but in this case, the success probability is not fixed since we are drawing without replacement. The Poisson distribution is used to model the count of rare events in a fixed interval of time, which is not applicable in this scenario. Therefore, the best choice is the hypergeometric distribution.

Question 5

In a binomial distribution,
A)the variable X is continuous.
B)the probability of event of interest π is stable from trial to trial.
C)the number of trials n must be at least 30.
D)the results of one trial are dependent on the results of the other trials.

Accepted Answer

In a binomial distribution, the probability of the event of interest π is stable from trial to trial. The variable X is discrete, not continuous. The number of trials n does not necessarily have to be at least 30. The results of one trial are independent of the results of the other trials.

Question 6

The covariance
A)must be between -1 and +1.
B)must be positive.
C)can be positive or negative.
D)must be less than +1.

Accepted Answer

The covariance is a measure of how two variables vary together. It can take negative, positive, or zero values, indicating that the variables either vary in opposite directions, in the same direction, or are not related to each other, respectively. Therefore, option A, B, and D are incorrect as they suggest that the covariance has certain restrictions or conditions that do not apply.

Question 7

If the outcomes of a variable follow a Poisson distribution,then their
A)mean equals the standard deviation.
B)median equals the standard deviation.
C)mean equals the variance.
D)median equals the variance.

Accepted Answer

In a Poisson distribution, the mean equals the variance. The standard deviation can be calculated as the square root of the variance. Therefore, the mean does not necessarily equal the standard deviation or the median, and the median does not equal the variance.

Question 8

A campus program evenly enrolls undergraduate and graduate students.If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building,what is the probability that all 4 students selected are undergraduate students?
A)0.0256
B)0.0625
C)0.16
D)1.00

Accepted Answer

There are a total of 2 groups of students: undergraduate and graduate. The probability of selecting an undergraduate student is 1/2, and since there are no restrictions on the sampling, this probability remains the same for each selection. Therefore, the probability of selecting 4 undergraduate students in a row is (1/2)^4 = 1/16 = 0.0625.

Question 9

Whenever π = 0.5,the binomial distribution will
A)always be symmetric.
B)be symmetric only if n is large.
C)be right-skewed.
D)be left-skewed.

Accepted Answer

When π = 0.5, the binomial distribution is always symmetric regardless of the value of n. This is because the probability of success and failure is the same, so the distribution will have a symmetric bell shape.

Question 10

If n = 10 and π = 0.70,then the standard deviation of the binomial distribution is
A)0.07.
B)1.45.
C)7.00.
D)14.29.

Accepted Answer

The standard deviation of a binomial distribution is given by the formula σ = √(npq), where n is the number of trials, p is the probability of success, and q is the probability of failure. Plugging in n = 10 and π = 0.70, we get:

σ = √(10*0.7*0.3) = 1.449...

Rounding to two decimal places, we get σ ≈ 1.45, so the best choice is (B).

Question 11

What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem? An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims.It is known that the industry proportion for false claims is 3%.The consulting firm has decided to randomly and independently sample 100 of the company's insurance claims.They believe the number of these 100 that are false will yield the information the company desires.
A)Binomial distribution
B)Poisson distribution
C)Hypergeometric distribution
D)None of the above

Accepted Answer

The situation described fits the criteria for a binomial distribution, as the sample size is fixed at 100, the trials are independent, there are only two possible outcomes (false or not false), and the probability of success (a false claim) is known and constant at 3%.

Question 12

What type of probability distribution will most likely be used to analyze the number of cars with defective radios in the following problem? From an inventory of 48 new cars being shipped to local dealerships,corporate reports indicate that 12 have defective radios installed.The sales manager of one dealership wants to predict the probability out of the 8 new cars it just received that,when each is tested,no more than 2 of the cars have defective radios.
A)Binomial distribution
B)Poisson distribution
C)Hypergeometric distribution
D)None of the above

Accepted Answer

The answer of What type of probability distribution will most...

Question 13

A professor receives,on average,24.7 e-mails from students the day before the midterm exam.To compute the probability of receiving at least 10 e-mails on such a day,he will use what type of probability distribution?
A)Binomial distribution
B)Poisson distribution
C)Hypergeometric distribution
D)None of the above.

Accepted Answer

The Poisson distribution is used to model the probability of a certain number of events occurring in a fixed interval of time or space, when the events are rare and randomly distributed. In this case, the professor receives e-mails from students, and the number of e-mails can be modeled by a Poisson distribution because they are randomly distributed and the rate of incoming e-mails is constant over time. Therefore, the best choice is the Poisson distribution.

Question 14

What type of probability distribution will most likely be used to analyze the number of blue chocolate chips per bag in the following problem? The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.When the production process is in control,the average number of blue chocolate chips per bag is 6.0.The manager is interested in analyzing the probability that any particular bag being inspected has fewer than 5.0 blue chocolate chips.
A)Binomial distribution
B)Poisson distribution
C)Hypergeometric distribution
D)None of the above

Accepted Answer

The Poisson distribution is used to analyze the number of events that occur in a specific time interval or space when the average rate of occurrence is known. In this problem, the average number of blue chocolate chips per bag is given and the manager is interested in the probability of a certain number of blue chocolate chips, which suggests a Poisson distribution is the most appropriate choice. The other options (Binomial and Hypergeometric distributions) are used for situations with finite populations and trials, which do not fit this problem.

Question 15

If n = 10 and π = 0.70,then the mean of the binomial distribution is
A)0.07.
B)1.45.
C)7.00.
D)14.29.

Accepted Answer

The answer of If n = 10 and π =...

Question 16

The portfolio expected return of two investments
A)will be higher when the covariance is zero.
B)will be higher when the covariance is negative.
C)will be higher when the covariance is positive.
D)does not depend on the covariance.

Accepted Answer

The answer of The portfolio expected return of two investments
A)will...

Question 17

What type of probability distribution will most likely be used to analyze warranty repair needs on new cars in the following problem? The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days.Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05.The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.
A)Binomial distribution
B)Poisson distribution
C)Hypergeometric distribution
D)None of the above

Accepted Answer

The problem involves a fixed sample size (20 new cars sold) and a probability of success (0.05 probability of needing a warranty repair). The manager is interested in predicting the number of warranty repairs in the next 90 days, which is a count of successes (cars needing a repair) out of a fixed sample size. Therefore, the problem fits the characteristics of a binomial distribution.

Question 18

The connotation "expected value" or "expected gain" from playing roulette at a casino means
A)the amount you expect to "gain" on a single play.
B)the amount you expect to "gain" in the long run over many plays.
C)the amount you need to "break even" over many plays.
D)the amount you should expect to gain if you are lucky.

Accepted Answer

Expected value or expected gain in the context of gambling refers to the average amount a player can expect to win or lose over many plays. It takes into account the probability of winning or losing and the amount of money at stake. Therefore, option B is the correct choice as it refers to the amount a player expects to gain in the long run over many plays, considering the odds of winning and the house edge.

Question 19

Whenever π = 0.1 and n is small,the binomial distribution will be
A)symmetric.
B)right-skewed.
C)left-skewed.
D)None of the above.

Accepted Answer

When π (the probability of success) is small and n is small, the binomial distribution will be right-skewed. This is because as n gets smaller, the distribution becomes more sensitive to extreme values (e.g. a single success or failure can have a bigger impact on the overall distribution). Additionally, when π is small, the probability of success is low, so there will be more failures and the distribution will be skewed towards the right.

Question 20

Which of the following about the binomial distribution is not a true statement?
A)The probability of the event of interest must be constant from trial to trial.
B)Each outcome is independent of the other.
C)Each outcome may be classified as either "event of interest" or "not event of interest."
D)The variable of interest is continuous.

Accepted Answer

The binomial distribution is applicable to discrete variables, not continuous ones. Therefore, statement D is not true.

Quiz 5: Discrete Probability Distributions

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR) .In 180 days of school,about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

A probability distribution is an equation that

A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.025.To find the probability that exactly 20 of the computers will require repair on a given day,one will use what type of probability distribution?

In a binomial distribution,

The covariance

If the outcomes of a variable follow a Poisson distribution,then their

Whenever π = 0.5,the binomial distribution will

If n = 10 and π = 0.70,then the standard deviation of the binomial distribution is

A professor receives,on average,24.7 e-mails from students the day before the midterm exam.To compute the probability of receiving at least 10 e-mails on such a day,he will use what type of probability distribution?

If n = 10 and π = 0.70,then the mean of the binomial distribution is

The portfolio expected return of two investments

The connotation "expected value" or "expected gain" from playing roulette at a casino means

Whenever π = 0.1 and n is small,the binomial distribution will be

Which of the following about the binomial distribution is not a true statement?