Q: In a bag with 3 red and 2 blue marbles, what is the probability of drawing a red marble?

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

Q: If a data set has a mean of 100 and a standard deviation of 20, what is the coefficient of variation (CV)?

$$CV = \frac{20}{100} \times 100 = 20\%$$

Q: A boxplot has Q1 = 10, Q3 = 30, and IQR = 20. What is the upper fence for outliers?

$$\text{Upper fence} = Q3 + 1.5 \times IQR = 30 + 1.5 \times 20 = 60$$

Q: A password must contain 3 letters followed by 2 digits. How many possible passwords are there if each letter and digit can be used more than once?

$$26 \times 26 \times 26 \times 10 \times 10 = 1,757,600$$

Q: In a lottery, the odds against winning are 49:1. What is the probability of winning?

$$P(\text{win}) = \frac{1}{50}$$

Q: A bag contains 4 red and 6 green marbles. If two marbles are drawn one after another without replacement, what is the probability both are red?

$$\frac{4}{10} \times \frac{3}{9} = \frac{12}{90} = \frac{2}{15}$$

Question 1

A researcher surveys 50 people at a local coffee shop about their favorite beverage. Which of the following best describes the sample and the population in this study?

Accepted Answer

Sample: 50 people surveyed at the coffee shop; Population: all coffee drinkers in the city

Question 2

Which type of bias is most likely present if a survey about political opinions is conducted only among attendees at a political rally?

Accepted Answer

Undercoverage bias

Question 3

A data set records the number of books read by each student in a class. How would you classify this variable?

Accepted Answer

Quantitative, discrete, ratio

Question 4

Which sampling method is used when a researcher randomly selects several classrooms and surveys every student in those classrooms?

Accepted Answer

Cluster sampling

Question 5

Which graph is most appropriate for displaying the distribution of monthly rainfall over a 10-year period?

Accepted Answer

Time series (line graph)

Question 6

A set of exam scores has a mean of 80 and a standard deviation of 5. A student scores 90. What is the z-score for this student?

Accepted Answer

$$z = \frac{90 - 80}{5} = 2$$

Question 7

Given the data set: 2, 4, 6, 8, 10, 12, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 10 - 4 = 6$$

Question 8

A data set has a mean of 50 and a median of 40. What is the likely shape of the distribution?

Accepted Answer

Likely skewed right

Question 9

In a bag with 3 red and 2 blue marbles, what is the probability of drawing a red marble?

Accepted Answer

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

Question 10

A student scores 70 on a test where the mean is 60 and the standard deviation is 5. According to the empirical rule, what percent of students scored between 55 and 65?

Accepted Answer

About 68%

Question 11

If a data set has a mean of 100 and a standard deviation of 20, what is the coefficient of variation (CV)?

Accepted Answer

$$CV = \frac{20}{100} 	imes 100 = 20\%$$

Question 12

A boxplot has Q1 = 10, Q3 = 30, and IQR = 20. What is the upper fence for outliers?

Accepted Answer

$$	ext{Upper fence} = Q3 + 1.5 	imes IQR = 30 + 1.5 	imes 20 = 60$$

Question 13

A password must contain 3 letters followed by 2 digits. How many possible passwords are there if each letter and digit can be used more than once?

Accepted Answer

$$26 	imes 26 	imes 26 	imes 10 	imes 10 = 1,757,600$$

Question 14

A committee of 4 is to be chosen from 10 people. How many ways can this be done?

Accepted Answer

$$10 	ext{C} 4 = 210$$

Question 15

In a lottery, the odds against winning are 49:1. What is the probability of winning?

Accepted Answer

$$P(	ext{win}) = \frac{1}{50}$$

Question 16

A survey asks, 'Do you support freedom for the region?' Which bias is most likely present?

Accepted Answer

Wording bias

Question 17

A bag contains 4 red and 6 green marbles. If two marbles are drawn one after another without replacement, what is the probability both are red?

Accepted Answer

$$\frac{4}{10} 	imes \frac{3}{9} = \frac{12}{90} = \frac{2}{15}$$

Question 18

A student flips a coin 4 times. What is the probability of getting at least one head?

Accepted Answer

$$1 - (\frac{1}{2})^4$ = 1 - \frac{1}{16} = \frac{15}{16}$$

Question 19

A data set has a mean of 70. If a value is at the 80th percentile, what does this mean?

Accepted Answer

80% of the values are less than this value

Introductory Statistics: Exam 1 Study Guide (Plain-English Edition)

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