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.

Question 2

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

Accepted Answer

The random variable must 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 calculates the mean $$\mu of a $$discrete probability distribution?

Accepted Answer

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

Question 6

If the variance $$\$$sigma^2$$ for the number of females in two births 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 for the number of females in two births if $$\mu = 1.0$$ and $$\sigma = 0.7$$?

Accepted Answer

$$2.4 or $$higher

Question 8

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

Accepted Answer

Both A and B.

Question 9

Which of the following is the formula for the variance $$\$$sigma^2$$ of a discrete probability distribution?

Accepted Answer

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

Question 10

If you bet $$5 on the number 7 in roulette, with a probability of losing 5$ being $$\frac{37}{38}$$ and a probability of winning 175$ being $$\frac{1}{38}$, what is the expected value of your bet?

Accepted Answer

$$-0.26$$

Question 11

Which of the following best describes the rare event rule for inferential statistics?

Accepted Answer

If an outcome is very unlikely under a given assumption and it occurs, the assumption is probably not correct.

Question 12

Which of the following is true about expected value in the context of probability distributions?

Accepted Answer

It represents the long-term average outcome of a random variable.

Question 13

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

Accepted Answer

$$x is a $$significantly high value.

Question 14

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

Accepted Answer

$$1.00$$

Question 15

Which of the following scenarios describes a continuous random variable?

Accepted Answer

The body temperature of a randomly selected person.

Question 16

If the probability of an event is negative, what does this indicate?

Accepted Answer

There is a calculation error, as probabilities cannot be negative.

Question 17

Which of the following is a valid interpretation of the standard deviation $$\sigma in a $$probability distribution?

Accepted Answer

It measures the spread of the values around the mean.

Question 18

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

Accepted Answer

$$[0.3, 1.7]$$

Probability Distributions: Concepts, Calculations, and Applications

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