Q: A frequency distribution has classes 10-19, 20-29, 30-39, and 40-49. What is the class width?

$$\text{class width} = 20 - 10 = 10$$

Q: A deck of 52 cards is shuffled. What is the probability of drawing an ace on the first draw?

$$P(\text{ace}) = \frac{4}{52} = \frac{1}{13}$$

Q: A test for a rare disease is positive for 95% of people with the disease and 10% of people without it. If 2% of the population has the disease, what is the probability a randomly selected person who tests positive actually has the disease? (Assume 10,000 people.)

$$P(\text{disease} | \text{positive}) = \frac{190}{190 + 980} \approx 0.162$$

Q: A password consists of 2 letters followed by 3 digits. Letters and digits may repeat. How many passwords are possible?

$$26 \times 26 \times 10 \times 10 \times 10 = 676,000$$

Q: A machine has 4 independent parts, each working with probability 0.95. What is the probability that at least one part works?

$$P(\text{at least one works}) = 1 - (0.05)^4$ = 1 - 0.00000625 = 0.99999375$$

Question 1

Which of the following best describes a parameter in statistics?

Accepted Answer

A numerical measure describing an entire population.

Question 2

A researcher wants to study the effect of a new drug. She randomly assigns patients to receive either the drug or a placebo, and neither the patients nor the doctors know which group each patient is in. Which two features of good experimental design are illustrated?

Accepted Answer

Randomization and blinding

Question 3

Which level of measurement allows meaningful ratios and has a true zero point?

Accepted Answer

Ratio

Question 4

A frequency distribution has classes 10-19, 20-29, 30-39, and 40-49. What is the class width?

Accepted Answer

$$	ext{class width} = 20 - 10 = 10$$

Question 5

A histogram of household incomes is right-skewed. Which measure of center is most affected by the skew?

Accepted Answer

Mean

Question 6

Given the data set: 4, 7, 7, 10, 12, 15, what is the sample standard deviation? (Round to two decimal places.)

Accepted Answer

$$s = \sqrt{\frac{(4-9)^2$ + (7-9)^2$ + (7-9)^2$ + (10-9)^2$ + (12-9)^2$ + (15-9)^2$}{6-1}} = \sqrt{\frac{25 + 4 + 4 + 1 + 9 + 36}{5}} = \sqrt{\frac{79}{5}} \approx 3.98$$

Question 7

A value of 85 comes from a data set with mean 70 and standard deviation 10. What is the z-score for 85?

Accepted Answer

$$z = \frac{85 - 70}{10} = 1.5$$

Question 8

The five-number summary for exam scores is: minimum 40, Q1 60, median 75, Q3 90, maximum 120. What is the interquartile range (IQR)?

Accepted Answer

$$	ext{IQR} = 90 - 60 = 30$$

Question 9

According to the empirical rule, what percentage of values in a bell-shaped distribution fall within 2 standard deviations of the mean?

Accepted Answer

95%

Question 10

A boxplot shows a maximum value above the upper outlier fence. According to the 1.5 × IQR rule, what does this indicate?

Accepted Answer

The maximum is a potential outlier.

Question 11

A scatterplot of hours studied and exam score shows points closely clustered along a line sloping upward. What is the likely value of the correlation coefficient $$r$$?

Accepted Answer

$$r = 0.90$$

Question 12

A survey asks students to rate cafeteria food as 'poor', 'fair', 'good', or 'excellent'. What is the level of measurement?

Accepted Answer

Ordinal

Question 13

A random sample of 50 patients is selected from a hospital with 1,000 patients. The mean blood pressure of the sample is 120 mmHg. What is this mean called?

Accepted Answer

A statistic

Question 14

A deck of 52 cards is shuffled. What is the probability of drawing an ace on the first draw?

Accepted Answer

$$P(	ext{ace}) = \frac{4}{52} = \frac{1}{13}$$

Question 15

Two events, A and B, are independent. If $$P(A) = 0.5$$ and $$P(B) = 0.2$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$P(A 	ext{ and } B) = 0.1$$

Question 16

A test for a rare disease is positive for 95% of people with the disease and 10% of people without it. If 2% of the population has the disease, what is the probability a randomly selected person who tests positive actually has the disease? (Assume 10,000 people.)

Accepted Answer

$$P(	ext{disease} | 	ext{positive}) = \frac{190}{190 + 980} \approx 0.162$$

Question 17

How many ways can 5 books be arranged on a shelf?

Accepted Answer

$$5! = 120$$

Question 18

A committee of 4 is to be chosen from 12 people. How many different committees are possible?

Accepted Answer

$$12C4 = \frac{12!}{4!\,8!} = 495$$

Question 19

A password consists of 2 letters followed by 3 digits. Letters and digits may repeat. How many passwords are possible?

Accepted Answer

$$26 	imes 26 	imes 10 	imes 10 	imes 10 = 676,000$$

Question 20

A machine has 4 independent parts, each working with probability 0.95. What is the probability that at least one part works?

Accepted Answer

$$P(	ext{at least one works}) = 1 - (0.05)^4$ = 1 - 0.00000625 = 0.99999375$$

Step-by-Step Guidance for MAT-181 Midterm (Elementary Statistics, Chapters 1-4)

Study Guide - Practice Questions

Study Guide - Flashcards