Q: A factory produces light bulbs. The probability that a bulb is defective is $$0.05. If $$two bulbs are selected at random, what is the probability that both are defective? $$P( ext{both defective}) = P( ext{defective}) \times P( ext{defective})$$

$$P = 0.05 \times 0.05 = 0.0025$$

Q: A data set has values: 12, 15, 18, 21, 24. What is the percentile rank of the value 18? Percentile rank formula: $$\frac{\text{number of values below}}{\text{total number of values}} \times 100$$

$$\frac{2}{5} \times 100 = 40\%$$

Question 1

Which of the following is an example of data measured at the interval level?

Accepted Answer

The temperature in Celsius recorded each hour during a day.

Question 2

A researcher wants to study the average income of residents in a city. She divides the city into neighborhoods and randomly selects some neighborhoods, then surveys all residents in those neighborhoods. Which sampling method is she using?

Accepted Answer

Cluster sampling

Question 3

Which of the following best describes continuous data?

Accepted Answer

The height of students measured in centimeters.

Question 4

Given the following frequency distribution, what is the class midpoint for the class 20–29?

Class: 10–19, 20–29, 30–39
Frequency: 5, 8, 7

Accepted Answer

24.5

Question 5

A frequency histogram is constructed for a set of exam scores. Which of the following statements is TRUE?

Accepted Answer

The bars should touch each other, and the horizontal axis can be scaled using class midpoints or boundaries.

Question 6

Given the following data: 2, 4, 6, 8, 10. What is the mean using the formula $$\bar{x} = \frac{\sum x}{n}$$?

Accepted Answer

$$\bar{x} = 6$$

Question 7

A distribution of test scores is described as 'skewed right.' Which of the following is most likely TRUE?

Accepted Answer

The mean is greater than the median.

Question 8

Given the data set: 5, 7, 7, 8, 10, what is the mode?

Accepted Answer

7

Question 9

If the standard deviation of a data set is $$s = 4$$, what is the variance?

Accepted Answer

$$16$$

Question 10

Given the data set: 3, 5, 7, 9, 11. What is the z-score for the value 9? Use $$\bar{x} = 7$$, $$s = 3$$.

$$z = \frac{x - \bar{x}}{s}$$

Accepted Answer

$$z = \frac{9 - 7}{3} = \frac{2}{3} \approx 0.67$$

Question 11

A student scored a z-score of $$z = -2.5 on a $$standardized test. Which statement is most accurate?

Accepted Answer

The student's score is significantly low compared to the mean.

Question 12

In a class of 30 students, 6 received an A. What is the probability that a randomly selected student received an A?

$$P(A) = \frac{	ext{number of A's}}{	ext{total students}}$$

Accepted Answer

$$P(A) = \frac{6}{30} = 0.2$$

Question 13

A deck of cards contains 52 cards. What is the probability of drawing a heart OR a king?

$$P(	ext{heart OR king}) = P(	ext{heart}) + P(	ext{king}) - P(	ext{heart AND king})$$

Accepted Answer

$$P = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = 0.3077$$

Question 14

A factory produces light bulbs. The probability that a bulb is defective is $$0.05. If $$two bulbs are selected at random, what is the probability that both are defective?

$$P(	ext{both defective}) = P(	ext{defective}) 	imes P(	ext{defective})$$

Accepted Answer

$$P = 0.05 	imes 0.05 = 0.0025$$

Question 15

In a group of 10 people, what is the probability that at least one person has blood type O if the probability that a person has blood type O is $$0.4$$?

$$P(	ext{at least one}) = 1 - P(	ext{none})$$

Accepted Answer

$$P = 1 - (0.6$$)^{10}$$ \approx 0.994$$

Question 16

A data set has values: 12, 15, 18, 21, 24. What is the percentile rank of the value 18?

Percentile rank formula: $$\frac{	ext{number of values below}}{	ext{total number of values}} 	imes 100$$

Accepted Answer

$$\frac{2}{5} 	imes 100 = 40\%$$

Question 17

A researcher uses systematic sampling to select every 10th patient from a list of 500. Which statement is TRUE?

Accepted Answer

Systematic sampling selects subjects at regular intervals from an ordered list.

Question 18

Given the following data: 4, 8, 12, 16, 20. Calculate the standard deviation using the formula:

$$s = \sqrt{\frac{n \sum x^2$ - (\sum x)^2$}{n(n-1)}}$$

Where $$n = 5.$$

Accepted Answer

Question 19

A hospital administrator wants to compare patient satisfaction scores between male and female patients. She randomly selects 50 males and 50 females from the patient database. Which sampling method is she using?

Accepted Answer

Stratified sampling

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