Q: In a deck of 52 playing cards, what is the probability of drawing a heart OR a king?

$$P(\text{heart}) + P(\text{king}) - P(\text{heart and king}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$$

Q: A fair coin is tossed three times. What is the probability of getting at least one head?

$$1 - P(\text{no heads}) = 1 - (\frac{1}{2})^3$ = 1 - \frac{1}{8} = \frac{7}{8}$$

Q: A student wants to know the probability of randomly selecting a red marble from a bag containing 3 red, 5 blue, and 2 green marbles. What is the probability?

$$P(\text{red}) = \frac{3}{3+5+2} = \frac{3}{10}$$

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

$$\frac{\text{number of values less than 18}}{\text{total number of values}} \times 100 = \frac{2}{5} \times 100 = 40\%$$

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 hospital wants to estimate the average recovery time for patients after surgery. They divide patients into age groups and randomly select patients from each group. Which sampling method is being used?

Accepted Answer

Stratified sampling

Question 3

Which of the following best describes a continuous variable?

Accepted Answer

The height of students measured in centimeters.

Question 4

Given the following frequency distribution for exam scores:

Class: 60-69, Frequency: 3
Class: 70-79, Frequency: 5
Class: 80-89, Frequency: 7
Class: 90-99, Frequency: 2

What is the class midpoint for the class 80-89?

Accepted Answer

$$\frac{80+89}{2} = 84.5$$

Question 5

A frequency histogram is constructed for a set of test scores. Which of the following is NOT a correct guideline for constructing the histogram?

Accepted Answer

Leave gaps between the bars to show separation between classes.

Question 6

Given the following data set: 2, 4, 6, 8, 10. What is the midrange?

Accepted Answer

$$\frac{2+10}{2} = 6$$

Question 7

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

Accepted Answer

The mean is greater than the median.

Question 8

Given the following frequencies and midpoints:

Class Midpoints: 10, 20, 30
Frequencies: 2, 3, 5

Calculate the mean using the formula $$\bar{x} = \frac{\sum(f \cdot x)}{\sum f}.$$

Accepted Answer

$$\bar{x} = \frac{(2 \cdot 10) + (3 \cdot 20) + (5 \cdot 30)}{2+3+5} = \frac{20+60+150}{10} = \frac{230}{10} = 23$$

Question 9

A student scored 85 on a test where the mean was 80 and the standard deviation was 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 80}{5} = 1$$

Question 10

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

Accepted Answer

$$4^2 = 16$

Question 11

A data set has $$n = 5$$ values: 2, 4, 6, 8, 10. Calculate the sample standard deviation using the formula $$s = \sqrt{\frac{n \sum x^2$ - (\sum x)^2$}{n(n-1)}}.$$

Accepted Answer

$$s = \sqrt{\frac{5 \cdot (2^2$+4^2+6^2$+8^2+10^2$) - (2+4+6+8+10)^2$}{5 \cdot 4}} = \sqrt{\frac{5 \cdot 220 - 30^2$}{20}} = \sqrt{\frac{1100 - 900}{20}} = \sqrt{10} \approx 3.16$$

Question 12

A value is considered significantly low if its z-score is less than -2. If the mean is 50 and the standard deviation is 10, which of the following values is significantly low?

Accepted Answer

25

Question 13

In a deck of 52 playing cards, what is the probability of drawing a heart OR a king?

Accepted Answer

$$P(	ext{heart}) + P(	ext{king}) - P(	ext{heart and king}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$$

Question 14

A fair coin is tossed three times. What is the probability of getting at least one head?

Accepted Answer

$$1 - P(	ext{no heads}) = 1 - (\frac{1}{2})^3$ = 1 - \frac{1}{8} = \frac{7}{8}$$

Question 15

A medical researcher selects every 10th patient from a list of 500 patients. Which sampling method is used?

Accepted Answer

Systematic sampling

Question 16

A student wants to know the probability of randomly selecting a red marble from a bag containing 3 red, 5 blue, and 2 green marbles. What is the probability?

Accepted Answer

$$P(	ext{red}) = \frac{3}{3+5+2} = \frac{3}{10}$$

Question 17

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

Accepted Answer

$$\frac{	ext{number of values less than 18}}{	ext{total number of values}} 	imes 100 = \frac{2}{5} 	imes 100 = 40\%$$

Question 18

A teacher records the following test scores: 70, 75, 80, 85, 90. What is the range?

Accepted Answer

$$90 - 70 = 20$$

Question 19

A researcher wants to select a sample of students from a university. She randomly selects 4 entire dormitories and surveys all students in those dorms. Which sampling method is this?

Accepted Answer

Cluster sampling

Introductory Statistics: Exam 1 Study Guide

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