Practice identifying, interpreting, and calculating probabilities for common probability distributions.
Read each problem carefully. Show your work in the space provided. Round decimal answers to three decimal places unless otherwise stated.
Modeling outcomes with discrete and continuous distributions
Statistics - Grade 9-12
- 1
A random variable X has the following probability distribution: P(X = 0) = 0.10, P(X = 1) = 0.25, P(X = 2) = 0.40, and P(X = 3) = 0.25. Verify that this is a valid probability distribution.
- 2
Using the distribution P(X = 0) = 0.10, P(X = 1) = 0.25, P(X = 2) = 0.40, and P(X = 3) = 0.25, find the expected value of X.
- 3
A fair six-sided die is rolled once. Let X be the number rolled. What type of probability distribution does X have, and what is P(X = 4)?
- 4
A bag contains 5 red marbles and 3 blue marbles. One marble is selected at random. Let X = 1 if the marble is red and X = 0 if the marble is blue. Give the probability distribution of X.
- 5
A basketball player makes 70% of free throws. If the player shoots 5 free throws, what is the probability that the player makes exactly 4? Assume each shot is independent.
- 6
A multiple-choice quiz has 10 questions, each with 4 answer choices. A student guesses on every question. Let X be the number of correct answers. Identify the distribution and state n and p.
- 7
For a binomial random variable with n = 8 and p = 0.25, find the mean and standard deviation.
- 8
A factory finds that 2% of light bulbs are defective. If 12 bulbs are randomly selected, what is the probability that none are defective? Assume independence.
- 9
A spinner has four equal sections labeled A, B, C, and D. It is spun 20 times. Which distribution would model the number of times the spinner lands on A, and why?
- 10
In a geometric distribution, the probability of success on each trial is p = 0.20. What is the probability that the first success occurs on the 4th trial?
- 11
A customer service center receives an average of 6 calls per hour. If calls follow a Poisson distribution, what is the probability of receiving exactly 4 calls in one hour?
- 12
The number of emails a teacher receives during lunch follows a Poisson distribution with a mean of 3. What is the variance of this distribution?
- 13
Scores on a test are normally distributed with a mean of 75 and a standard deviation of 10. Find the z-score for a student who scored 90.
- 14
Heights of adult women in a town are normally distributed with a mean of 64 inches and a standard deviation of 3 inches. About what percent of adult women are between 61 and 67 inches tall?
- 15
A continuous random variable is uniformly distributed from 0 to 10. What is the probability that a randomly selected value is between 3 and 7?