Free Printable Distributions (Uniform, Binomial, Poisson, Normal)

Worksheets

Distributions (Uniform, Binomial, Poisson, Normal)

Total questions: 25

Worksheet time: 6hrs 15mins

Name

Class

Date

Is the distribution below a probability distribution? Why or why not?

Yes. All P(x) values are between 0 and 1, and ∑P(x) = 1

No, not all P(x) values are between 0 and 1.

No, ∑P(x) ≠ 1.

For all distributions, what is the relationship standard deviation, s.d., and variance?

$s.d.=\sqrt[]{var}$

$var=\sqrt[]{s.d.}$

$var=\frac{1}{\sigma}$

$s.d.=var^2$

This distribution allows us to model the number of successes, (which are discrete data) after a fixed number of trials, given a certain probability of success. This distribution assumes that each trial is independent.

For example, the probabilities of getting 3 heads, 2 heads, 1 head, or no heads if you flip a coin 10 times.

Uniform Distribution

Binomial Distribution

Normal Distribution

Poisson Distribution

This distribution allows us to model a situation where a certain number of events (which is discrete data) happen over a specified time or distance interval. It is used to predict the amount of variation from a known average rate of occurrence within a given time or distance frame.

There is not a fixed number of events, so there is no ceiling on the number of events we can have.

Uniform Distribution

Binomial Distribution

Normal Distribution

Poisson Distribution

Which of the following is NOT an assumption of the Binomial distribution?

All trials must be independent.

Each trial must be classified as a success or a failure.

All trials are dependent on each other.

The number of successes in the trials is counted.

What is the expected value, E(x), for a binomial distribution?

E(x) = n · p

E(x) = n · 𝜎

$E\left(x\right)=n\cdot\sigma^2$

$E\left(x\right)=n\cdot p^2$

What is the variance for a binomial distribution?

$\sigma^2=n\cdot p\left(1-p\right)$

$\sigma^2=n\cdot p$

$\sigma^2=n\cdot p\left(1+p\right)$

What is an interesting feature of the Poisson distribution?

The variance = the mean

The variance = the standard deviation

The variance = 1

What is the expected value of a Poisson distribution?

$E\left(x\right)=avg\ rate,\ \lambda$

$E\left(x\right)=n\cdot p\left(1-p\right)$

$E\left(x\right)=\sigma$

10.

Which one of these variables is a continuous random variable?

The time it takes a randomly selected student to complete an exam.

The number of tattoos a randomly selected person has.

The number of women taller than 68 inches in a random sample of 5 women.

The number of correct guesses on a multiple choice test.

11.

What type of distribution models this scenario?

The mean number of accidents per month at a certain intersection is 3. What is the probability that in any given month exactly 4 accidents will occur at this intersection?

Uniform

Binomial

Poisson

Normal

12.

What TYPE of distribution would model this scenario:

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school of 2000 people. What's the probability that exactly 100 people have Type B blood?

Uniform

Binomial

Poisson

Normal

13.

What type of statistical distribution allows us to model events where the outcome is discrete, and each outcome has an equally likely chance of occurring.

For example, rolling a 6-sided die once and each outcome is equally likely.

Uniform Distribution

Binomial Distribution

Normal Distribution

Poisson Distribution

14.

This distribution allows us to model a continuous random variable where the further away from the mean you are, the less likely the outcome. It is defined by a mean and a standard deviation. It is symmetric in shape, and the mean, median, and mode are equal.

Uniform Distribution

Binomial Distribution

Normal Distribution

Poisson Distribution

15.

Choose the correct sign

"probability of more than 7"

P(X>7)

P(X<7)

P(X≥7)

P(X≤7)

16.

Choose the correct sign

"probability of less than 7"

P(X>7)

P(X<7)

P(X≥7)

P(X≤7)

17.

Choose the correct sign

"probability of at least 7"

P(X>7)

P(X<7)

P(X≥7)

P(X≤7)

18.

Choose the correct sign

"probability of at most 7"

P(X>7)

P(X<7)

P(X≥7)

P(X≤7)

19.

Choose the correct sign

"probability of between 4 and 9"

P(4<X<9)

P(4<X≤9)

P(4≤X≤9)

P(4≤X<9)

20.

Choose the correct sign

"probability of less than 7"

P(X>7)

P(X<7)

P(X≥7)

P(X≤7)

21.

Binomial Distribution: The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school.What is the probability that exactly 2 of the first 20 blood donors have Type B blood?

0.316

0.282

0.001

Not here

22.

Poisson Distribution:

The mean number of accidents per month at a certain intersection is 3. What is the probability that in any given month exactly 4 accidents will occur at this intersection?

0.815

0.647

0.168

0.352

23.

The normal curve is symmetrical about the mean.

True

False

24.

Which graphs given are left skewed?

25.

Which of the distributions given are right skewed?

100 %

Distributions (Uniform, Binomial, Poisson, Normal)

Total questions: 25

Worksheet time: 6hrs 15mins

Similar Resources on Wayground