Free Practice Quiz Question List

3 Probability Distributions Online Quiz Questions

Use this free practice quiz with 20 questions to review 3 Probability Distributions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

For a random variable with cumulative distribution function $F(x)=P(X\le x)$ , what does $F(7)$ represent?

A
The probability that the variable is exactly 7
B
The probability that the variable is at most 7
C
The probability that the variable is greater than 7
D
The probability that the variable is at least 7

True or false

1 point

For a continuous random variable, the probability of taking any one exact value is 0.

A
True
B
False

Choose one

1 point

Delivery times are continuous and reasonably symmetric and bell-shaped. Which distribution best fits this description?

A
Normal distribution
B
Binomial distribution
C
A discrete distribution without a specified model
D
A binomial distribution with a success probability that changes between trials

Choose all

1 point

Select all conditions required for a binomial model of the number of successes.

A
A fixed number of trials is set in advance.
B
The probability of success may vary from trial to trial.
C
Trials are independent.
D
Each trial has two mutually exclusive outcomes.
E
Trials must have exactly the same outcome each time.
F
The probability of success is the same on every trial.

True or false

1 point

For a normal distribution, about 95% of values fall within 2 standard deviations of the mean.

A
True
B
False

Fill in the blank

1 point

Complete the definition of the cumulative distribution function: $F(x)=P(X$ $x)$ .

Written response

1 point

A fixed batch contains 20 independent orders, each with a return probability of 0.15. What is the expected number of returned orders?

Fill in the blank

1 point

For a binomial random variable with $n$ trials and success probability $p$ , the standard deviation is .

Choose one

1 point

Delivery time is modeled as normal with mean 30 minutes and standard deviation 5 minutes. What is the z-score for a delivery time of 40 minutes?

A
-2
B
1
C
2
D
10

Written response

1 point

Each of 10 independent orders has a return probability of 0.10. What is the probability that exactly 2 orders are returned? Round your answer to three decimal places.

Choose all

1 point

Select all situations that can appropriately be modeled with a binomial distribution.

A
Counting returns among 50 independent orders when each order has the same known return probability
B
Modeling delivery times that are continuous and bell-shaped
C
Counting successful quality checks in 25 independent checks with the same success probability
D
Counting successes across trials whose success probabilities change from trial to trial

Open ended

1 point

A business wants to estimate both the number of returned orders in a fixed batch and the chance that delivery time exceeds a target. Explain which distribution could be used for each quantity and state the relevant assumptions or calculation approach.

Choose one

1 point

A discrete random variable has a probability mass function. Which statement must be true across all possible values of the variable?

A
The values of a probability mass function sum to 0.
B
The probabilities assigned by a probability mass function across all possible values sum to 1.
C
A probability mass function describes only interval areas under a continuous curve.
D
A probability mass function gives the probability of every real number in a range.

Choose one

1 point

Which statement about a normal distribution is correct?

A
The total area under its curve is 1.
B
It assigns positive probability to every exact value of a continuous variable.
C
It can only represent discrete counts.
D
Its mean must always equal 0.

Written response

1 point

A delivery time is $40$ minutes, and delivery times are modeled with mean $30$ minutes and standard deviation $5$ minutes. Using $z=\frac{x-\mu}{\sigma}$ , what is the delivery time's z-score?

Choose one

1 point

A retailer records the number of orders returned in one day and the delivery time for each order. Which classification fits these quantities?

A
The number of returned orders is discrete; delivery time is continuous.
B
The number of returned orders is continuous; delivery time is discrete.
C
Both quantities are discrete.
D
Both quantities are continuous.

Choose one

1 point

In a binomial model for five orders, let a returned order count as a success. When finding the probability of exactly two returns, what does $C(5,2)$ count?

A
The different orders in which two returned orders can be arranged.
B
The different ways to choose which two of the five orders are returned.
C
The probability that all five orders are returned.
D
The number of orders that are not returned.

Choose one

1 point

Two normal distributions have the same mean. Distribution A has standard deviation $2$ , and Distribution B has standard deviation $6$ . Which statement compares them correctly?

A
Distribution A has a larger spread because its standard deviation is smaller.
B
Both distributions have different centers because their standard deviations differ.
C
Distribution B has a larger spread, while both distributions have the same center.
D
Both distributions have the same spread because their means are equal.

True or false

1 point

A probability distribution can support statistical analysis, but its assumptions should be reasonable for the situation being modeled.

A
True
B
False

Written response

1 point

Delivery time is modeled by a normal distribution with mean $30$ minutes and standard deviation $5$ minutes. What delivery time is two standard deviations above the mean? Give your answer in minutes.