Question 1

Which of the following best describes a discrete random variable?

Accepted Answer

A variable that has a finite or countable number of possible values, such as the number of heads in 10 coin tosses.

Question 2

Which of the following is NOT a requirement for a probability distribution?

Accepted Answer

The random variable can be categorical.

Question 3

Given the probability histogram for the number of females in two births, what is the probability of having exactly one female?

Accepted Answer

$$0.50$$

Question 4

Suppose $$x is $$the number of females in two births. What is the expected value (mean) $$\mu of$$ $$x$$?

Accepted Answer

$$\mu = 1.0$$

Question 5

Which formula correctly represents the mean $$\mu of a $$discrete probability distribution?

Accepted Answer

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

Question 6

If the variance $$\$$sigma^2$$ of a probability distribution is 0.5$, what is the standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = 0.7$$

Question 7

Using the range rule of thumb, which value would be considered significantly high if $$\mu = 1.0$$ and $$\sigma = 0.7$$?

Accepted Answer

$$2.4$$

Question 8

A probability distribution has $$P(0) = 0.25$$, $$P(1) = 0.50$$, and $$P(2) = 0.25. $$What is $$\sum P(x)$$?

Accepted Answer

$$1.00$$

Question 9

Which of the following scenarios describes a continuous random variable?

Accepted Answer

The height of students in a classroom.

Question 10

If $$P(x 	ext{ or more}) \leq 0.05$$, what can you conclude about $$x$$?

Accepted Answer

$$x is a $$significantly high value.

Question 11

A table lists countries and the proportion of unlicensed software in each. Why does this NOT describe a probability distribution?

Accepted Answer

The values of $$x$$ are not numerical and the probabilities do not sum to 1.

Question 12

Which formula is used to calculate the variance $$\$$sigma^2$$ of a discrete probability distribution?

Accepted Answer

$$\$$sigma^2$$ = \sum (x - \mu)^2$ \cdot P(x)$$

Question 13

If the probability of an event is very small and the event occurs, what does the rare event rule suggest?

Accepted Answer

The assumption about the probability is probably not correct.

Question 14

Which of the following is the best interpretation of expected value in a probability distribution?

Accepted Answer

The mean value expected over a large number of trials.

Question 15

If $$\mu = 1.0$$ and $$\sigma = 0.7$$, what is the range of values that are NOT significant according to the range rule of thumb?

Accepted Answer

$$0.3 \leq x \leq 2.4$$

Question 16

Which of the following is a valid probability value for a probability distribution?

Accepted Answer

$$0.8$$

Question 17

A student claims that the probability distribution for the number of heads in two coin tosses is $$P(0) = 0.3$$, $$P(1) = 0.5$$, $$P(2) = 0.3. $$What is wrong with this distribution?

Accepted Answer

The sum of the probabilities is not 1.

Question 18

Which of the following best describes a probability histogram?

Accepted Answer

A graph where the vertical scale shows probabilities for each value of a random variable.

Probability Distributions: Concepts, Parameters, and Significance

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