Free Practice Quiz Question List

05 Common Statistical Distributions Online Quiz Questions

Use this free practice quiz with 20 questions to review 05 Common Statistical Distributions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which situation is most appropriately modeled by a binomial distribution?

A
The number of trials required to obtain the first success
B
The number of successes in a fixed number of independent trials
C
A continuous measurement equally likely throughout an interval
D
A standardized value from a normal distribution

True or false

1 point

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

A
True
B
False

Choose one

1 point

What does a geometric random variable represent?

A
The number of successes in $n$ trials
B
Any real value in a finite interval
C
The number of trials through the first success
D
A value with mean zero and standard deviation one

Written response

1 point

A component has a defect probability of $p=0.02$ , and 50 components are inspected independently. If $X$ is the number of defective components, what is $E(X)$ ? Enter the numerical value.

Fill in the blank

1 point

For a binomial model, the number of trials must be , and the success probability must be from trial to trial.

Choose all

1 point

Select all statements that are true for a normal distribution.

A
It is symmetric about its mean.
B
It is bell-shaped.
C
Every normal distribution has mean zero.
D
Its mean, median, and mode are equal.

True or false

1 point

When approximating $P(X=k)$ for a binomial random variable with a normal distribution, the continuity-correction interval is $[k-0.5,k+0.5]$ .

A
True
B
False

Choose one

1 point

A waiting time $X$ is uniformly distributed on $[0,10]$ minutes. What is $P(2\le X\le4)$ ?

A
0.02
B
0.12
C
0.20
D
0.80

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? Enter the numerical value.

Fill in the blank

1 point

The standard normal distribution has mean and standard deviation .

Choose all

1 point

Select all conditions or procedures that support a normal approximation to a binomial distribution.

A
$np\ge10$
B
$n(1-p)\ge10$
C
The binomial trials must be dependent.
D
A continuity correction of 0.5 is used.

Open ended

1 point

Explain the difference between a discrete random variable and a continuous random variable. Include the role of a PMF or PDF and explain how probabilities are assigned in each case.

Choose one

1 point

A customer independently makes a purchase with probability $0.20$ on each visit. What is the probability that the first purchase occurs on the fourth visit?

A
0.0200
B
0.1024
C
0.1600
D
0.4096

Choose one

1 point

If $X$ is binomial and $Y$ is its normal approximation, which expression applies the continuity correction when approximating $P(X\ge k)$ ?

A
$P(Y\ge k-0.5)$
B
$P(Y\ge k+0.5)$
C
$P(Y\le k-0.5)$
D
$P(Y\le k+0.5)$

Choose one

1 point

A quality-control process examines a fixed number of independent components. Each component is either defective or not defective, and the probability of a defect is constant. Which distribution models the number of defective components?

A
Geometric distribution
B
Binomial distribution
C
Uniform distribution
D
Normal distribution

True or false

1 point

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

A
True
B
False

Choose one

1 point

Adult heights are modeled by $X\sim N(68,3^2)$ , with height measured in inches. What is the z-score for an adult who is 74 inches tall?

A
$z=1$
B
$z=\frac{3}{2}$
C
$z=2$
D
$z=6$

Written response

1 point

A trial has an independent success probability of $p=0.25$ on each attempt. If $X$ is the number of trials through the first success, what is $E(X)$ ?

Choose one

1 point

A customer makes an independent purchase with probability $p=0.20$ on each visit. What is the probability that the first purchase occurs on the fourth visit?

A
0.0200
B
0.0800
C
0.1024
D
0.2000

Written response

1 point

What is the name of the geometric-distribution property stating that, after several failures, the probability of needing more than an additional $t$ trials is unchanged?