Q: For a binomial distribution with $$n=6$$ and $$p=0.1$$, what is the standard deviation?

$$\sqrt{npq} = \sqrt{6 \times 0.1 \times 0.9} = 0.735$$

Question 1

Which of the following is a requirement for a discrete probability distribution?

Accepted Answer

Each outcome must be mutually exclusive, and the sum of all probabilities must equal 1.

Question 2

Given the probability distribution for Olive Garden’s group sizes, what is the expected group size?

Accepted Answer

3.56 people

Question 3

Which formula correctly calculates the mean (expected value) of a discrete probability distribution?

Accepted Answer

$$\sum\limits_{i=1}^{n} x_i P(x_i)$$

Question 4

A business calculates the expected monetary value (EMV) for a project with three possible outcomes: $$120,000 (probability 0.25), 100$$,000 (probability 0.60), and $90,000 (probability 0.15). What is the EMV?

Accepted Answer

$$\103$$,500$

Question 5

Which formula is used to calculate the variance of a discrete probability distribution using the shortcut method?

Accepted Answer

$$\sum\limits_{i=1}^{n} x_i^2$ P(x_i) - \mu^2$

Question 6

In a binomial experiment, which of the following is NOT a characteristic?

Accepted Answer

The probability of success changes from trial to trial.

Question 7

If the probability of a customer buying a product after sampling is 0.20, and three customers are sampled, what is the probability that exactly one customer buys the product?

Accepted Answer

0.384

Question 8

Which formula represents the probability of observing exactly $$x$$ successes in $$n$$ binomial trials?

Accepted Answer

$$\frac{n!}{(n-x)!x!} p^x q$$^{n-x}$$

Question 9

For a binomial distribution with $$n=6$$ and $$p=0.1$$, what is the standard deviation?

Accepted Answer

$$\sqrt{npq} = \sqrt{6 	imes 0.1 	imes 0.9} = 0.735$$

Question 10

Which scenario best fits the use of a Poisson distribution?

Accepted Answer

Counting the number of customers arriving at a store in an hour.

Question 11

If the average number of no-show customers at a salon is 4.2 per Saturday, what is the probability that exactly 2 customers will miss their appointments next Saturday (using the Poisson formula)?

Accepted Answer

0.1323

Question 12

Which formula is used to calculate the probability of $$x$$ occurrences in a Poisson distribution?

Accepted Answer

$$\frac{\lambda^x e$$^{-\lambda}$$}{x!}$$

Question 13

When can the Poisson distribution be used to approximate the binomial distribution?

Accepted Answer

When $$n \geq 20$$ and $$p \leq 0.05$$

Question 14

Which of the following is a characteristic of the hypergeometric distribution?

Accepted Answer

Sampling is done without replacement.

Question 15

A retailer has 22 employees, 8 of whom are older than 55. If 7 employees are randomly laid off, what is the probability that 5 of them are older employees (using the hypergeometric formula)?

Accepted Answer

$$\frac{\binom{8}{5} \binom{14}{2}}{\binom{22}{7}}$$

Question 16

Which formula calculates the mean of a hypergeometric distribution?

Accepted Answer

$$\mu = n \frac{R}{N}$$

Question 17

Which Excel function would you use to calculate the probability of exactly $$x$$ successes in a hypergeometric distribution?

Accepted Answer

HYPGEOM.DIST(x, n, R, N, FALSE)

Question 18

Which of the following best describes the difference between discrete and continuous random variables?

Accepted Answer

Discrete random variables have a finite number of outcomes, while continuous random variables have an infinite number of outcomes.

Discrete Probability Distributions: Concepts, Calculations, and Applications

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