Free Practice Quiz Question List

6 Common Probability Models Online Quiz Questions

Use this free practice quiz with 20 questions to review 6 Common Probability Models, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which quantity is most naturally modeled as a continuous random variable?

A
The number of defective items in a sample
B
The measurement error of a device
C
The number of customers arriving in an hour
D
The number of trials before the first success

True or false

1 point

True or false: If $X$ is a continuous random variable, then $P(X=a)=0$ for every single value $a$ .

A
True
B
False

Written response

1 point

A support center makes independent calls, each with the same probability of resolving a customer's issue. Which distribution models the number of calls required until the first resolution?

Fill in the blank

1 point

Complete the two binomial-model conditions: There must be a of trials, and the trials must be .

Choose one

1 point

A box contains 12 light bulbs, 3 of which are defective. Four bulbs are selected without replacement, and the number of defective bulbs is recorded. Which probability model is most appropriate?

A
A fixed number of independent trials with the same success probability
B
The waiting time until the first success
C
Sampling a finite population without replacement and counting successes
D
The number of events in a time interval with a stable average rate

Choose all

1 point

Which two conditions are required for a standard binomial model? Select all correct choices.

A
There are exactly $n$ trials.
B
The waiting process must continue until the first success.
C
The trials are independent, or sufficiently close to independent.
D
The event rate must be constant over a time interval.

True or false

1 point

True or false: If $X\sim\operatorname{Poisson}(\lambda)$ , then $E(X)=\operatorname{Var}(X)=\lambda$ .

A
True
B
False

Written response

1 point

Adult heights are modeled by $X\sim N(68,3^2)$ , where height is measured in inches. What is the z-score for a height of 74 inches?

Fill in the blank

1 point

The exponential distribution models a waiting time until the next event in a Poisson process and has the .

Choose one

1 point

A bus arrives at a random time during a 12-minute interval, with all arrival times equally likely. What is the probability that the waiting time is no more than 3 minutes?

A
0.10
B
0.25
C
0.50
D
0.75

Choose all

1 point

Which two scenarios are naturally modeled by a geometric or negative binomial distribution? Select all correct choices.

A
The number of trials needed to obtain the first success
B
The number of successes in 20 independent trials
C
The number of trials needed to obtain the fifth success
D
The number of successes in a sample drawn without replacement

Open ended

1 point

A quality inspector selects several items from a finite shipment without replacement and counts the defective items. Explain why the hypergeometric distribution is appropriate, how its assumptions differ from those of the binomial distribution, and when a binomial approximation might be reasonable.

Choose one

1 point

Which statement best describes the central limit theorem for a sample mean based on independent observations with mean $\mu$ and standard deviation $\sigma$ ?

A
It becomes exactly uniform regardless of the population.
B
Its standard deviation becomes $\sigma\sqrt{n}$ .
C
It becomes approximately normal under suitable conditions, with standard deviation $\frac{\sigma}{\sqrt{n}}$ .
D
It must have the same distributional shape as the original population.

Choose one

1 point

Which statement about a continuous random variable is correct?

A
A continuous random variable must have a probability greater than zero at every exact value.
B
For a continuous random variable, the probability of any single exact value is zero.
C
A continuous random variable can take only a finite number of values.
D
A continuous random variable must have equal probability on every interval of the same length.

True or false

1 point

True or false: Selecting 10 items without replacement from a small shipment and counting the defective items is automatically a binomial experiment.

A
True
B
False

Choose one

1 point

A website observes whether each of 200 independently selected visitors makes a purchase, with the same purchase probability for every visitor. Which probability model describes the number of purchases?

A
Binomial
B
Geometric
C
Poisson
D
Exponential

Choose one

1 point

A box contains 30 components, 6 of which are defective. Four components are selected without replacement, and the number of defectives is recorded. Which model is most appropriate?

A
Binomial
B
Poisson
C
Hypergeometric
D
Uniform

Choose one

1 point

For a Poisson random variable with rate parameter $\lambda$ , which statement about its mean and variance is correct?

A
Its mean is $\lambda$ and its variance is $\lambda^2$ .
B
Its mean and variance are both $\lambda$ .
C
Its mean is $\frac{1}{\lambda}$ and its variance is $\frac{1}{\lambda^2}$ .
D
Its mean is zero and its variance is $\lambda$ .

Written response

1 point

Adult heights are modeled by $X\sim N(68,3^2)$ inches. What is the z-score for a height of 74 inches?

Written response

1 point

A count of successes is modeled by $X\sim\operatorname{Binomial}(12,0.25)$ . What is the expected number of successes?