Question 1

Which of the following best describes the random variable 'number of bottles of juice sold in a cafeteria during lunch'?

Accepted Answer

Discrete

Question 2

Given the probability histogram shown, what is the probability that a randomly selected family with three children has exactly 2 boys?

Accepted Answer

$$0.38$$

Question 3

Which of the following is NOT a requirement for a probability distribution for a discrete random variable $$x$$?

Accepted Answer

The mean must be greater than the standard deviation

Question 4

A probability distribution for a random variable $$x is $$given as follows: $$P(5) = 0.10$$, $$P(10) = -0.30$$, $$P(15) = 0.50$$, $$P(20) = 0.70. $$Does this form a valid probability distribution?

Accepted Answer

No, because one probability is negative

Question 5

If the mean number of cheesecakes sold in a day is $$13.75$$, which formula was used to calculate this expected value?

Accepted Answer

$$E(x) = \sum x \cdot P(x)$$

Question 6

A family has three children. Assuming boys and girls are equally likely, what is the probability that the family has exactly 1 boy?

Accepted Answer

$$0.38$$

Question 7

Which of the following scenarios describes a binomial experiment?

Accepted Answer

Flipping a coin 10 times and counting the number of heads

Question 8

A quiz consists of 10 multiple choice questions, each with five possible answers. If a student guesses on all questions, what is the probability that the student will get at least 6 correct answers?

Accepted Answer

$$0.006$$

Question 9

For a Poisson distribution with mean $$\lambda = 3$$, what is the probability that exactly 7 students arrive during an office hour?

Accepted Answer

$$0.0216$$

Question 10

Suppose the number of goals scored at a soccer game follows a Poisson process with a goal scored every 18 minutes. If a game lasts 90 minutes, what is the standard deviation of the mean number of goals scored during a game?

Accepted Answer

$$2.34$$

Question 11

Given the probability histogram for the number of boys in a family with three children, what is the mean number of boys?

Accepted Answer

$$1.50$$

Question 12

If $$x is a $$Poisson random variable with $$\lambda = 1.2$$, what is the expected value $$E(x)$$?

Accepted Answer

$$1.2$$

Question 13

A sandwich shop records the number of condiments used for a hamburger. If the mean is $$1.14$$ and the standard deviation is $$1.04$$, which formula is used to calculate the standard deviation for a discrete probability distribution?

Accepted Answer

$$\sigma = \sqrt{\sum (x - \mu)^2$ P(x)}$$

Question 14

Which of the following statements about the Poisson distribution is correct?

Accepted Answer

The mean and variance are equal

Question 15

If a random variable $$x$$ has the following probability distribution: $$x = 0, 1, 2, 3$$ with $$P(x) = 0.1, 0.4, 0.4, 0.1$$, what is the probability that $$x is at $$least 2?

Accepted Answer

$$0.5$$

Constructing and Interpreting a Probability Distribution for Discrete Random Variables

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