Q: A sample of 100 digital voice recorders contains 15 defective units. What is the probability that a randomly selected unit is NOT defective?

$$P(\text{not defective}) = \frac{85}{100}$$

Q: If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, are events A and B independent?

Yes, because $$P(A \cap B) = P(A) \times P(B)$$

Q: A player bets $$7 on $$the number $$13 in $$roulette and has a $$\frac{1}{38}$$ probability of winning. If the metal ball lands on $$13$$, the player gets to keep the $$7$$ plus the gain of $$245. $$What is the expected value of the game for the player?

$$E = 245 \times \frac{1}{38} + (-7) \times \frac{37}{38}$$

Question 1

A researcher collects the ages of all members of the U.S. Senate. Is this data a sample or a population?

Accepted Answer

Population, because it includes all members of the Senate.

Question 2

Which of the following variables is qualitative?

Accepted Answer

The color of a car.

Question 3

A study records the number of heartbeats per minute for a group of adults. Without performing any calculations, which measure of central tendency best represents the projected data, and why?

Accepted Answer

The mean, because the data are interval.

Question 4

Given the following frequency distribution for ages in a town, approximate the mean age:

$$\begin{array}{cc}
	ext{Age} & 	ext{Frequency} \
0-9 & 20 \
10-19 & 40 \
20-29 & 60 \
30-39 & 50 \
40-49 & 30 \
50-59 & 10 \
\end{array}$$

Which formula should you use?

Accepted Answer

$$\bar{x} = \frac{\sum f m}{\sum f}$$

Question 5

A certain brand of automobile tire has a mean life span of 24,000 miles and a standard deviation of 2,250 miles. What is the $$z-$$score for a tire that lasted 30,000 miles?

Accepted Answer

$$z = \frac{30,000 - 24,000}{2,250}$$

Question 6

A probability experiment consists of rolling a fair six-sided die. What is the probability of rolling a number greater than 2?

Accepted Answer

$$\frac{4}{6}$$

Question 7

In a stadium of 4000 people, 27% are cheering for Team A and 25% are female. If 8% are both female and cheering for Team A, what is the probability that a randomly selected individual is either female or cheering for Team A?

Accepted Answer

$$0.27 + 0.25 - 0.08$$

Question 8

A DJ is preparing a playlist of 20 songs. How many different ways can the DJ choose the first five songs to play?

Accepted Answer

$$P(20, 5) = \frac{20!}{(20-5)!}$$

Question 9

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

Accepted Answer

Each probability must be a positive number.

Question 10

In a binomial distribution with $$n = 5$$ and $$p = 0.3$$, what is the expected value $$E(x)$$?

Accepted Answer

$$E(x) = n \cdot p = 5 \cdot 0.3 = 1.5$$

Question 11

A sample of 100 digital voice recorders contains 15 defective units. What is the probability that a randomly selected unit is NOT defective?

Accepted Answer

$$P(	ext{not defective}) = \frac{85}{100}$$

Question 12

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, are events A and B independent?

Accepted Answer

Yes, because $$P(A \cap B) = P(A) 	imes P(B)$$

Question 13

A player bets $$7 on $$the number $$13 in $$roulette and has a $$\frac{1}{38}$$ probability of winning. If the metal ball lands on $$13$$, the player gets to keep the $$7$$ plus the gain of $$245. $$What is the expected value of the game for the player?

Accepted Answer

$$E = 245 	imes \frac{1}{38} + (-7) 	imes \frac{37}{38}$$

Question 14

Which of the following best describes an observational study?

Accepted Answer

The researcher observes and measures characteristics without attempting to influence the outcome.

Question 15

Given the following data set: $$2, 4, 6, 8, 10, 12, 14, 16, 18, 20$$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 15 - 5 = 10$$

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