Business Analytics Chapter 4: Probability: An Introduction to Modeling Uncertainty

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive-thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order? a. 0.4866 b. 0.6321 c. 0.1813 d. 0.7769

a. 0.4866

What is the total area under the normal distribution curve? a. 1 b. It must be calculated c. It depends upon the mean and standard deviation d. 100

a. 1

The _____ probability distribution can be used to estimate the number of vehicles that go through an intersection during the lunch hour. a. Poisson b. normal c. triangular d. binomial

a. Poisson

Bayes' theorem is a method used to compute _____ probabilities. a. conditional b. posterior c. prior d. empirical

a. conditional

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order? a. f(x)=(2/3)e^(-2/3x) b. f(x)=(1/3)e^(-x/3) c. f(x)=(1/5)e^(-x/5) d. None of these choices are correct.

a. f(x)=(2/3)e^(-2/3x)

The center of a normal curve is _____. a. the mean of the distribution b. always a positive number c. equal to the standard deviation d. always equal to zero

a. the mean of the distribution

A survey of 100 random high school students finds that 85 students watched the Super Bowl, 25 students watched the Stanley Cup Finals, and 20 students watched both games. How many students did not watch either game? a. 30 b. 10 c. 20 d. 15

b. 10

A _____ describes the range and relative likelihood of all possible values for a random variable. a. probability mass function of an event b. probability distribution for a random variable c. density function d. probability

b. probability distribution for a random variable

The event containing the outcomes belonging to A or B or both is the _____ of A and B. a. intersection b. union c. Venn diagram d. complement

b. union

The random variable X is known to be uniformly distributed between 2 and 12. Compute the standard deviation of X. a. 3.464 b. 12 c. 2.887 d. 8.333

c. 2.887

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes in a day is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 13,000 steps. What was his percentile on that day? a. 99.7% b. 95% c. 97.7% d. 100%

c. 97.7%

Which of the following statements is correct? a. The binomial distribution is a continuous probability distribution, and the normal distribution is a discrete probability distribution. b. The binomial and normal distributions are both discrete probability distributions. c. The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution. d. The binomial and normal distributions are both continuous probability distributions.

c. The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.

A variable that can only take on specific numeric values is called a _____. a. categorical variable b. continuous random variable c. discrete random variable d. complex random variable

c. discrete random variable

A variable that can only take on specific numeric values is called a _____. a. complex random variable b. categorical variable c. discrete random variable d. continuous random variable

c. discrete random variable

Probability is the _____. a. number of successes divided by the standard deviation of the distribution b. chance that an event will not happen c. numerical measure of the likelihood that an event will occur d. number of successes divided by the number of failures

c. numerical measure of the likelihood that an event will occur

An initial estimate of the probabilities of events is a _____ probability. a. posterior b. empirical c. prior d. conditional

c. prior

The triangular distribution is a good model for _____ distributions. a. normal b. uniform c. skewed d. poisson

c. skewed

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution? a. 10,000 b. 7,533 c. 8,078 d. 12,467

d. 12,467

The number of minutes that Samantha waits to catch the bus is uniformly distributed between 0 and 15 minutes. What is the probability that Samantha has to wait less than 4.5 minutes to catch the bus? a. 10% b. 3% c. 20% d. 30%

d. 30%

Which of the following is not a characteristic of the normal probability distribution? a. The distribution is symmetrical. b. The mean, median, and the mode are equal. c. The mean of the distribution can be negative, zero, or positive. d. The standard deviation must be 1.

d. The standard deviation must be 1.

If a z-score is zero, then the corresponding x-value must be equal to the _____. a. mode b. standard deviation c. median d. mean

d. mean

The triangular distribution is a good model for _____ distributions. a. normal b. poisson c. uniform d. skewed

d. skewed

All the events in the sample space that are not part of the specified event are called _____. a. joint events b. simple events c. independent events d. the complement of the event

d. the complement of the event