Question 1

In a Poisson distribution, the probability of success may vary from trial to trial.

Accepted Answer

In a Poisson distribution, the probability of success is constant for all trials, and the distribution describes the number of occurrences of an event in a fixed interval of time or space.

Question 2

To construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial.

Accepted Answer

This is correct as these are the two main parameters required to construct a binomial distribution.

Question 3

The binomial probability distribution is always negatively skewed.

Accepted Answer

The binomial probability distribution is not always negatively skewed. It can be positively skewed or have a roughly symmetric shape depending on the values of the parameters (n and p) of the distribution.

Question 4

To construct a binomial probability distribution, the mean must be known.

Accepted Answer

The mean can be calculated from the formula for the binomial distribution, but it is not a requirement for constructing the distribution. The only required values are the number of trials and the probability of success on each trial.

Question 5

The mean of a binomial distribution is the product of n and π.

Accepted Answer

The mean of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of success (π), so the statement is true.

Question 6

The mean of a probability distribution is called its expected value.

Accepted Answer

The statement is true. The expected value of a probability distribution is the mean value of all possible outcomes weighted by their respective probabilities.

Question 7

The variance of a binomial distribution is found by nπ(1 - π).

Accepted Answer

This formula is correct and is used to calculate the variance of a binomial distribution where n is the number of trials and π is the probability of success on each trial.

Question 8

When sampling is done without replacement and the outcomes are measured as either a success or failure, the hypergeometric distribution should be applied.

Accepted Answer

The hypergeometric distribution should be used when sampling without replacement and the outcomes are measured as a success or failure.

Question 9

Judging from recent experience, 5% of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?

Accepted Answer

The probability of one keyboard being non-defective is 1 - 0.05 = 0.95. Since the keyboards are randomly selected, the probability of getting none of them defective is (0.95)^6, which is approximately 0.735. Therefore, the correct answer is C.

Question 10

The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.) for service is:  On a typical day, how many automobiles should Lakeside Olds expect to be lined up at opening time?

Accepted Answer

To find the expected number of automobiles lined up at opening time, we need to take a weighted average of the possible outcomes, where the weights are the probabilities of each outcome.

Expected value = (0)(0.05) + (1)(0.10) + (2)(0.15) + (3)(0.25) + (4)(0.20) + (5)(0.10) + (6)(0.05) = 2.85

Therefore, Lakeside Olds should expect around 2.85 automobiles to be lined up at opening time. The closest choice is C, 2.85.

Question 11

On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?

Accepted Answer

The answer of On a very hot summer day, 5%...

Question 12

The probability of a particular outcome must always be between 0.0 and 1.0 inclusive.

Accepted Answer

This is because probability is a measure of the likelihood of an event occurring, and it cannot be negative or greater than 1.

Question 13

A random variable represents the outcome of an experiment.

Accepted Answer

A random variable is a numerical quantity assigned to each result of an experiment, and typically represents a real-world observable event or measurement. Therefore, it does indeed represent the outcome of an experiment.

Question 14

If the variance is 3.6 grams, what is the standard deviation?

Accepted Answer

The standard deviation is the square root of the variance. 
√3.6 = 1.897, so the answer is B.

Question 15

A probability distribution is a mutually exclusive and collectively exhaustive listing of experimental outcomes that can occur by chance, and their corresponding probabilities.

Accepted Answer

The definition of a probability distribution includes that it must be mutually exclusive and collectively exhaustive, meaning that all possible outcomes are accounted for and no two outcomes can occur simultaneously. The listing also includes the probabilities associated with each outcome.

Question 16

The variance of a probability distribution is based on the sum or squared differences from the mean.

Accepted Answer

The variance is calculated by taking the sum of squared differences from the mean, divided by the number of observations.

Question 17

A total of 60% of the customers of a fast food chain order a hamburger, French fries, and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

Accepted Answer

We can model this situation using a binomial distribution with n = 15 and p = 0.6 (the probability of ordering the required food items). We are interested in finding the probability of getting at least 10 successes (orders of the required food items) in 15 trials. Using a calculator or software, we can find that P(X >= 10) = 0.403, which is the answer choice C. Therefore, the best choice is C.

Question 18

As a general rule of thumb, if the items selected for a sample are not replaced and the sample size is less than 5 percent of the population, the binomial distribution can be used to approximate the hypergeometric distribution.

Accepted Answer

This is a correct statement. When the items selected for a sample are not replaced and the sample size is less than 5 percent of the population, the binomial distribution can be used as an approximation of the hypergeometric distribution. This is because the binomial distribution assumes independence between trials, which is a reasonable assumption when the sample size is small in relation to the population size.

Question 19

The variance measures the skewness of a probability distribution.

Accepted Answer

The variance measures the spread or variability of a probability distribution, not the skewness.

Question 20

The random variable for a Poisson probability distribution can assume an infinite number of values.

Accepted Answer

This is true, as the Poisson distribution is a discrete probability distribution that can take on any non-negative integer value. As such, it technically has an infinite number of possible values.

Quiz 6: Discrete Probability Distributions