Question 1

Which of the following statements best describes a discrete random variable?

Accepted Answer

A variable whose values are finite or countable, such as the number of coin tosses before getting heads.

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 distribution for the number of females in two births: $$x = 0, 1, 2$$ with $$P(0) = 0.25$$, $$P(1) = 0.5$$, $$P(2) = 0.25$$, what is the mean ($$\mu) of $$the distribution?

Accepted Answer

$$\mu = 1.0$$

Question 4

Which formula is used to calculate the variance ($$\$$sigma^2$$) of a discrete probability distribution for manual calculations?

Accepted Answer

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

Question 5

A probability value in a distribution is calculated as $$0.000000123. $$When rounding for inclusion in a table, which notation should be used?

Accepted Answer

0+

Question 6

In the context of probability distributions, what is the expected value ($$E) of a $$discrete random variable $$x$$?

Accepted Answer

The mean value of the outcomes, calculated as $$E = \sum[x \cdot P(x)].$$

Question 7

Suppose a probability distribution has $$x$$ values that are all integers. According to the rounding-off rule, to how many decimal places should you round the mean ($$\mu$$)?

Accepted Answer

One decimal place.

Question 8

Given the probability distribution for the number of females in two births: $$x = 0, 1, 2$$ with $$P(0) = 0.25$$, $$P(1) = 0.5$$, $$P(2) = 0.25$$, calculate the variance ($$\$$sigma^2$$) using the manual calculation formula.

Accepted Answer

$$\$$sigma^2$$ = 0.5$$

Question 9

Which of the following best describes a probability histogram for a discrete random variable?

Accepted Answer

A graph where each bar is centered around the count and the vertical scale shows probabilities.

Question 10

If the mean ($$\mu) of a $$probability distribution is $$1.0$$ and the standard deviation ($$\sigma) is$$ $$0.7$$, according to the range rule of thumb, which value would be considered significantly high?

Accepted Answer

$$x \geq 2.4$$

Question 11

A country has a proportion of unlicensed software of $$0.70. $$Does this value satisfy the requirement for a probability distribution?

Accepted Answer

Yes, because $$0.70 is $$between $$0$$ and $$1$$ inclusive.

Question 12

If $$P(x 	ext{ or more}) \leq 0.05$$, what can be concluded about $$x in a $$probability distribution?

Accepted Answer

$$x is a $$significantly high value.

Question 13

Which of the following statements is TRUE regarding parameters and statistics in probability distributions?

Accepted Answer

The mean, variance, and standard deviation of a probability distribution are parameters.

Question 14

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

Accepted Answer

$$-0.4 \u003c x \u003c 2.4$$

Question 15

Which scenario describes a continuous random variable?

Accepted Answer

The body temperature of a patient measured in degrees Celsius.

Question 16

If the probability distribution for a random variable $$x$$ has $$\sum P(x) = 1.001$$, what should you conclude?

Accepted Answer

The distribution is valid because the sum is close to 1 and rounding errors are acceptable.

Question 17

A student claims that the mean of a probability distribution is always equal to the most probable value. Is this statement correct?

Accepted Answer

No, because the mean is the expected value, not necessarily the most probable value.

Question 18

If $$P(x 	ext{ or fewer}) \leq 0.05$$, what can be concluded about $$x in a $$probability distribution?

Accepted Answer

$$x is a $$significantly low value.

Question 19

Which formula correctly calculates the standard deviation ($$\sigma) of a $$discrete probability distribution?

Accepted Answer

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

Chapter 5

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드