Question 1

If the variance is 3.6 grams,what is the standard deviation?
A)0.600
B)1.897
C)6.000
D)12.96

Accepted Answer

The standard deviation is the square root of the variance, so we need to take the square root of 3.6. Using a calculator, we get the approximate answer of 1.897. Therefore, the best choice is B).

Question 2

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

Accepted Answer

This statement is true. The probability of an outcome can never be less than 0.0 or greater than 1.0, as the probability represents the likelihood of an event occurring, and it cannot be less likely than impossible (0.0) or more likely than certain (1.0).

Question 3

The variance measures the skewness of a probability distribution.

Accepted Answer

The variance measures the spread or dispersion of a probability distribution, not the skewness. Skewness is measured by the third standardized moment.

Question 4

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?
A)10.00
B)1.00
C)2.85
D)1.96

Accepted Answer

To find the expected value or mean of the probability distribution we need to multiply each outcome by its probability and then sum all the products. So,

Expected value = (0*0.06) + (1*0.08) + (2*0.11) + (3*0.25) + (4*0.2) + (5*0.1) + (6*0.05) + (7*0.015) + (8*0.01) + (9*0.005) + (10*0.005)

Expected value = 2.85

Therefore, Lakeside Olds should expect around 2.85 automobiles lined up at opening time on a typical day. The best choice among the given options is C.

Question 5

A random variable represents the outcome of an experiment.

Accepted Answer

This is true - a random variable is a variable that takes on different values with certain probabilities based on the outcome of an experiment.

Question 6

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

Accepted Answer

The Poisson distribution is used to model the likelihood of a certain number of events occurring in a fixed interval of time or space. The random variable in this distribution can take on any non-negative integer value, which is an infinite set of values, so the statement is true.

Question 7

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

A probability distribution is a listing of possible outcomes with their corresponding probabilities, and by definition, these outcomes must be mutually exclusive (i.e., they cannot occur at the same time) and collectively exhaustive (i.e., they must account for all possible outcomes).

Question 8

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?
A)1.000
B)0.186
C)0.403
D)0.000

Accepted Answer

We can use the binomial distribution formula with n = 15 and p = 0.6 (since 60% of customers order the three items).
P(X ≥ 10) = 1 - P(X < 10)
= 1 - Σ_(i=0)^9 (15 choose i) * (0.6)^i * (0.4)^(15-i)
Using a calculator, we get P(X ≥ 10) = 0.403, which corresponds to choice C.

Question 9

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

Accepted Answer

This is the formula for the variance of a binomial distribution.

Question 10

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?
A)0.002
B)0.344
C)0.599
D)0.100

Accepted Answer

The probability of a single employee not being absent is 95% (1 - 0.05). For 10 employees, the probability that none are absent is 0.95^10, which is approximately 0.599.

Question 11

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 statement is true. The binomial distribution is a discrete probability distribution that relates to the number of successes in a specified number of independent trials with a fixed probability of success for each trial. Therefore, the total number of trials and the probability of success for each trial are essential elements for constructing a binomial distribution.

Question 12

The binomial probability distribution is always negatively skewed.

Accepted Answer

The shape of the binomial probability distribution can vary depending on the values of the parameters (n and p). It can be symmetric, positively skewed, or negatively skewed.

Question 13

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

Accepted Answer

The mean of a binomial distribution can be calculated using the formula np, where n is the number of trials and p is the probability of success in each trial. However, it is not necessary to know the mean in order to construct a binomial probability distribution. Instead, the probabilities for each possible outcome can be calculated directly using the binomial formula.

Question 14

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

Accepted Answer

This statement accurately describes the calculation of variance. The formula for variance is Var(X) = ∑(x - μ)² P(x), where x is each possible outcome, μ is the mean, and P(x) is the corresponding probability. The calculation involves squaring the difference between each outcome and the mean, weighting these differences by their probability, and summing the results.

Question 15

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?
A)0.001
B)0.167
C)0.735
D)0.500

Accepted Answer

The probability of choosing a non-defective keyboard is 1 - 0.05 = 0.95. Since we are selecting six keyboards independently, the probability of all of them being non-defective is:

0.95 * 0.95 * 0.95 * 0.95 * 0.95 * 0.95 = 0.735

Therefore, the answer is (C) 0.735.

Question 16

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

Accepted Answer

The hypergeometric distribution is used for counting the number of successes in a fixed-sized sample drawn without replacement from a finite population, where the population size and number of successes are known. Hence, the given statement is true.

Question 17

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

Accepted Answer

In a Poisson distribution, the rate (mean number of occurrences in a fixed interval of time or space) is constant, implying that the probability of an event does not vary from trial to trial.

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% of the population,the binomial distribution can be used to approximate the hypergeometric distribution.

Accepted Answer

This statement is true. When the sample is taken without replacement and the sample size is less than 5% of the population, the binomial distribution can be used as an approximation of the hypergeometric distribution. This is because the probability of success does not change significantly from trial to trial since the sample size is small compared to the population size.

Question 19

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

Accepted Answer

The mean of a binomial distribution is nπ.

Question 20

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

Accepted Answer

This statement is true. The expected value of a probability distribution is the mean, which is calculated by summing the product of each outcome and its probability.

Quiz 6: Discrete Probability Distributions

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