Question 1

Which of the following is a key characteristic of a discrete random variable?

Accepted Answer

It has a finite or countable number of possible outcomes, usually whole numbers.

Question 2

Suppose a company tracks the number of customer complaints per day. Which type of probability distribution is most appropriate for modeling this data?

Accepted Answer

Discrete probability distribution

Question 3

Which of the following formulas correctly represents the mean (expected value) of a discrete probability distribution?

Accepted Answer

$$\mu = \sum x_i P(x_i)$$

Question 4

A manufacturer wants to know the expected monetary value (EMV) of profit from crop yield, given the following probabilities: Dry weather ($$200,000, 0.30$$), Light Rain ($$300,000, 0.50$$), Storm ($$150,000, 0.20). $$What is the EMV?

Accepted Answer

$$EMV = (200,000)(0.30) + (300,000)(0.50) + (150,000)(0.20) = 240,000$$

Question 5

Which of the following is NOT a requirement for a discrete probability distribution?

Accepted Answer

The outcomes must be measured on a continuous scale.

Question 6

A fair coin is tossed three times. What is the probability of getting exactly two heads?

Accepted Answer

$$P(X=2) = \binom{3}{2} (0.5)^2$ (0.5)^1$ = 0.375$$

Question 7

Which formula gives the variance of a discrete probability distribution?

Accepted Answer

$$\$$sigma^2$$ = \sum (x_i - \mu)^2$ P(x_i)$$

Question 8

A binomial experiment consists of 10 trials with probability of success $$p = 0.4. $$What is the mean and standard deviation of the number of successes?

Accepted Answer

$$\mu = np = 4.0$$, $$\sigma = \sqrt{npq} = 1.549$$

Question 9

Which scenario is best modeled by a Poisson distribution?

Accepted Answer

The number of customers arriving at a store per hour.

Question 10

A bank receives an average of 4 bad checks per week. What is the probability that it will receive exactly 3 bad checks next week? (Use the Poisson formula.)

Accepted Answer

$$P(3) = \frac{4^3$ e$$^{-4}$$}{3!} \approx 0.195$$

Question 11

Which of the following conditions must be met to use the Poisson distribution to approximate the binomial distribution?

Accepted Answer

The number of trials $$n \geq 20$$ and the probability of success $$p \leq 0.05.$$

Question 12

A random sample of 60 workers is taken from a factory where 3% are absent each day. What is the Poisson approximation for the probability that exactly one worker is absent?

Accepted Answer

$$P(1) = \frac{(1.8)^1$ e$$^{-1.8}$$}{1!} \approx 0.298$$

Question 13

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

Accepted Answer

=BINOM.DIST(x, n, p, FALSE)

Question 14

If the mean number of customer arrivals at a drive-through window is 12 per hour, what is the expected number of arrivals in 30 minutes?

Accepted Answer

6

Question 15

Which of the following statements about the variance of a Poisson distribution is correct?

Accepted Answer

The variance is equal to the mean: $$\$$sigma^2$$ = \lambda$$

Question 16

A store observes an average of 4.2 'no show' customers on Saturdays. What is the probability that exactly 2 customers will miss their appointment next Saturday? (Use Poisson distribution.)

Accepted Answer

$$P(2) = \frac{4.2^2$ e$$^{-4.2}$$}{2!}$$

Question 17

Which of the following is an example of a continuous random variable?

Accepted Answer

Time required to complete a task

Question 18

A lottery ticket costs $$3 and the probability of winning Lotto 6/49 on one play is 1/13$$,983,816$$. If you spend 300$ on tickets, what is the probability of winning at least once?

Accepted Answer

$$P(	ext{at least one win}) = 1 - (1 - \frac{1}{13,983,816}$$)^{100}$$

Discrete Probability Distributions: Study Notes for Business Statistics

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