Question 1

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

Accepted Answer

The standard deviation of a binomial distribution is calculated using the formula σ = sqrt(npq), where n is the sample size, p is the probability of success, and q is the probability of failure (q = 1-p). Plugging in the given values, we get σ = sqrt(10 * 0.70 * 0.30) = 1.45. Therefore, the best choice is B.

Question 2

In a game called Taxation and Evasion, a player rolls a pair of dice. If, on any turn, the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The probability that she does not get audited is ________.

Accepted Answer

0.2373

Question 3

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

Accepted Answer

The binomial distribution is a discrete probability distribution, meaning the variable of interest can only take on a finite number of values. Therefore, it is not continuous.

Question 4

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per
Week. Interpret this value.

Accepted Answer

The mean cost of $13.00 per week indicates the average cost of rats per week over the year.

Question 5

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.

Accepted Answer

The binomial distribution is appropriate here because the problem involves a fixed number of independent trials (100 claims), each with two possible outcomes (false claim or not), and a constant probability of success (3% false claims).

Question 6

A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What type of probability
Distribution can be used to figure out his chance of getting at least 20 questions right?

Accepted Answer

A binomial distribution is appropriate here because each question has two possible outcomes (correct or incorrect), there are a fixed number of questions (30), and the probability of getting a question right is constant (1/4).

Question 7

Whenever π = 0.5, the binomial distribution will

Accepted Answer

When π = 0.5, the binomial distribution is symmetric for any value of n. This is because the probability of success and failure are equal, resulting in a balanced distribution.

Question 8

A probability distribution is an equation that

Accepted Answer

A probability distribution assigns a particular probability of occurrence with each outcome, which is the definition given in option A. The other options are not accurate explanations of a probability distribution.

Question 9

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

Accepted Answer

When π = 0.1 and n is small, the binomial distribution will be right-skewed. This is because as n gets smaller, the distribution becomes more skewed towards the side with fewer successes. Since π is small, there will be fewer successes, and therefore the distribution will be skewed towards the right side.

Question 10

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

Accepted Answer

The mean of a binomial distribution is given by np, where n is the number of trials and p is the probability of success in each trial. 
Here, n = 10 and π = 0.70. 
So, the mean = np = 10 x 0.70 = 7.00. 
Hence, the best choice is C.

Question 11

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The probability that she gets audited once is ________.

Accepted Answer

The answer of In a game called Taxation and Evasion,...

Question 12

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?

Accepted Answer

The probability of selecting an undergraduate student is 0.5. For 4 students, the probability is (0.5)^4 = 0.0625.

Question 13

Another name for the mean of a probability distribution is its expected value.

Accepted Answer

This is true. The expected value and the mean are the same thing in a probability distribution.

Question 14

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.

Accepted Answer

The binomial distribution is appropriate here because it involves a fixed number of independent trials (20 cars), each with two possible outcomes (repair needed or not), and a constant probability of success (0.05).

Question 15

In a binomial distribution

Accepted Answer

In a binomial distribution, the probability of the event of interest π is stable from trial to trial. This means that the probability of success or failure remains the same for each trial, and the outcome of one trial does not influence the outcome of the other trials. The variable X in a binomial distribution is discrete, not continuous. There is no minimum number of trials required for a binomial distribution.

Question 16

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The probability that she gets audited at least once is ________.

Accepted Answer

The answer of In a game called Taxation and Evasion,...

Question 17

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution: $\begin{array}{lrrr}
\text { Price: } & \$ 10.00 & \$ 12.50 & \$ 15.00 \
\hline \text { Probability: } & 0.35 & 0.40 & 0.25
\end{array}$
 How much should the lab budget for next year's rat orders be, assuming this distribution does not
Change?

Accepted Answer

The answer of A lab orders 100 rats a week...

Question 18

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

Accepted Answer

"Expected value" or "expected gain" in roulette refers to the average amount of money a player can expect to win or lose over many plays. It takes into account the probability of winning or losing each bet, as well as the payout for each win. It is not the amount you expect to gain on a single play or the amount needed to break even, as these can vary greatly due to luck. The expected value is a long-term average, meaning the more plays a player makes, the closer their actual results should come to the expected value.

Question 19

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?

Accepted Answer

The binomial distribution is used because there are a fixed number of independent trials (125 computers), each with two possible outcomes (repair needed or not), and a constant probability of success (0.025).

Question 20

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?

Accepted Answer

The answer of Thirty-six of the staff of 80 teachers...

Quiz 5: Discrete Probability Distributions

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

In a game called Taxation and Evasion, a player rolls a pair of dice. If, on any turn, the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she does not get audited is ________.

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

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per Week. Interpret this value.

A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What type of probability Distribution can be used to figure out his chance of getting at least 20 questions right?

Whenever π = 0.5, the binomial distribution will

A probability distribution is an equation that

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

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

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited once is ________.

Another name for the mean of a probability distribution is its expected value.

In a binomial distribution

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited at least once is ________.

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

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?

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?