Free Practice Quiz Question List

5 Probability for Business Analytics Online Quiz Questions

Use this free practice quiz with 20 questions to review 5 Probability for Business Analytics, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

For a continuous random variable, the probability of observing any one exact value is zero. True or false?

A
True
B
False

Choose one

1 point

An event has probability $P(A)=0.27$ . What is the probability that the event does not occur?

A
0.27
B
0.73
C
1.00
D
0.54

Fill in the blank

1 point

Suppose $P(A)=0.4$ , $P(B)=0.5$ , and $P(A\cap B)=0.1$ . Find $P(A\cup B)$ :

Written response

1 point

A random payoff $X$ takes values 0, 2, and 4 units with probabilities 0.25, 0.50, and 0.25, respectively. What is $\operatorname{Var}(X)$ ?

Choose one

1 point

Which situation meets the defining assumptions for using a binomial distribution to count sales?

A
The number of events in an interval with a roughly stable average rate.
B
The number of successes in a fixed number of independent trials, each with the same success probability.
C
A continuous measurement modeled by a symmetric bell-shaped curve.
D
The outcome of a single trial with two possible results.

Choose all

1 point

Which statements describe the Poisson distribution? Select all that apply.

A
It can model a count of events in a fixed interval when the average rate is roughly stable and the assumptions are suitable.
B
Its mean and variance are both $\lambda$ , the expected count per interval.
C
It requires a fixed number of independent trials with the same success probability.
D
It is a continuous, symmetric, bell-shaped model.

Fill in the blank

1 point

If $P(A\cap B)=0.18$ and $P(B)=0.6$ , find $P(A\mid B)$ :

True or false

1 point

A random variable can have an expected value that is not one of its possible observed values. True or false?

A
True
B
False

Written response

1 point

A business wants to model the number of calls received in one hour, assuming a roughly stable average arrival rate and otherwise suitable model assumptions. Which distribution is a possible starting point?

Choose one

1 point

A decision-maker compares two options. Option A pays 100 with probability 0.6 and loses 50 with probability 0.4. Option B pays 60 for certain. Which option has the greater expected payoff?

A
Option A, with expected payoff 40.
B
Option B, with expected payoff 60.
C
They have equal expected payoffs.
D
There is not enough information to calculate either expected payoff.

Choose all

1 point

A business option has the greatest expected payoff among those considered. Which considerations could still affect whether it is the best choice? Select all that apply.

A
The decision-maker's tolerance for risk.
B
Cash constraints.
C
The possibility of severe downside outcomes.
D
The fact that the highest expected payoff guarantees the best actual result.

Open ended

1 point

A retailer estimates the current probability of a late delivery using last year's frequency, but operating conditions have changed. Explain why last year's estimate may be unrepresentative and describe two ways the retailer could obtain or assess a more relevant probability estimate.

Written response

1 point

A discrete random variable $X$ has probabilities $P(X=0)=0.2$ , $P(X=2)=0.5$ , and $P(X=5)=0.3$ . What is $F(2)=P(X\le 2)$ ?

Choose one

1 point

For which quantity is a normal model most likely to be unsuitable based on the stated context?

A
A measurement whose context and data support a symmetric, bell-shaped model.
B
An error measurement that is reasonably modeled as continuous and symmetric.
C
A strongly right-skewed demand quantity that cannot be negative.
D
A continuous measurement whose distribution is approximately symmetric.

Choose one

1 point

A business tracks whether one customer converts during a single visit, with conversion coded as 1 and no conversion as 0. Which distribution matches this one-trial process?

A
Bernoulli
B
Binomial
C
Poisson
D
Normal

True or false

1 point

A model estimates expected daily demand at 190 units. Does this guarantee that demand on each individual day will be exactly 190 units?

A
True
B
False

Choose one

1 point

Delivery time is modeled as a continuous random variable. What is the probability that a delivery takes exactly 2.5 days?

A
A probability equal to the density at that time
B
Zero
C
The probability of arriving within one day of that time
D
One

Choose one

1 point

Which situation is the clearest reason to avoid using a normal model without further justification?

A
Measurement errors that are approximately symmetric
B
A measurement supported by data and context as bell-shaped
C
Demand that is strongly right-skewed and cannot be negative
D
Values near a mean when a normal model is supported by the context

Choose one

1 point

Which business process satisfies the stated assumptions for modeling a success count with a binomial distribution?

A
The number of calls received in an hour at a roughly stable average rate
B
The number of conversions among 20 prospects when each has the same conversion probability and outcomes are independent
C
The delivery time, measured continuously in days
D
The outcome of one customer conversion trial coded as 0 or 1

Written response

1 point

Suppose $P(A\cap B)=0.12$ and $P(B)=0.30$ . What is the conditional probability $P(A\mid B)$ ? Enter the exact decimal value.