Q: A probability tree diagram shows the following probabilities: $$P(L) = 0.38$$, $$P(D|L) = 0.29$$, $$P(D|D) = 0.31. $$What is the probability of the sequence L-D?

$$P(L) \times P(D|L) = 0.38 \times 0.29 = 0.1102$$

Q: In a survey, 40% of respondents are male and 60% are female. If 10% of males and 5% of females own a pet snake, what is the probability that a randomly selected respondent owns a pet snake?

$$P(S) = 0.4 \times 0.10 + 0.6 \times 0.05 = 0.04 + 0.03 = 0.07$$

Question 1

Which of the following is an example of a statistic rather than a parameter?

Accepted Answer

The average height of a random sample of 100 students at a university.

Question 2

A variable that can take on any value within a given range is best described as:

Accepted Answer

Continuous

Question 3

Given the following frequency distribution, what is the cumulative percentage for the interval 84 to 85?

Interval: 78-79, 80-81, 82-83, 84-85, 86-87, 88-89, 90-91
Relative Frequency: 0.05, 0.10, 0.15, 0.17, 0.20, 0.11, 0.22

Accepted Answer

$$0.05 + 0.10 + 0.15 + 0.17 = 0.47 or$$ $$47\%$$

Question 4

Which of the following best describes a Pareto chart?

Accepted Answer

A bar graph with bars in descending order of frequency.

Question 5

A histogram of test scores is skewed right. Which of the following is true about the mean and median?

Accepted Answer

The mean is greater than the median.

Question 6

Given the following data set: $$3, 5, 7, 8, 10, 12, 15, 18, 20, 25$$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 17 - 6 = 11$$

Question 7

A sample of SAT scores has a mean of $$1100$$ and a standard deviation of $$150. $$What is the $$z-$$score for a student who scored $$1400$$?

Accepted Answer

$$z = \frac{1400 - 1100}{150} = 2$$

Question 8

Suppose you have two mutual funds, A and B. Fund A has a standard deviation of $$2.99$$ and Fund B has a standard deviation of $$5.59. $$Which statement is most accurate?

Accepted Answer

Fund A is more consistent in its returns than Fund B.

Question 9

A boxplot is most useful for displaying which of the following?

Accepted Answer

The five-number summary and potential outliers.

Question 10

If the mean of a data set is $$8.95$$ and the standard deviation is $$2.99$$, what is the range if the minimum is $$3$$ and the maximum is $$13.09$$?

Accepted Answer

$$Range = 13.09 - 3 = 10.09$$

Question 11

A probability tree diagram shows the following probabilities: $$P(L) = 0.38$$, $$P(D|L) = 0.29$$, $$P(D|D) = 0.31. $$What is the probability of the sequence L-D?

Accepted Answer

$$P(L) 	imes P(D|L) = 0.38 	imes 0.29 = 0.1102$$

Question 12

In a survey, 40% of respondents are male and 60% are female. If 10% of males and 5% of females own a pet snake, what is the probability that a randomly selected respondent owns a pet snake?

Accepted Answer

$$P(S) = 0.4 	imes 0.10 + 0.6 	imes 0.05 = 0.04 + 0.03 = 0.07$$

Question 13

If two events A and B are independent, which of the following must be true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 14

A basketball player has a probability of $$0.62 of $$making a free throw. What is the probability that the player misses both of two free throws?

Accepted Answer

$$(1 - 0.62) 	imes (1 - 0.62) = 0.38 	imes 0.38 = 0.1444$$

Question 15

Suppose you flip a fair coin three times. What is the probability of getting exactly two heads?

Accepted Answer

$$P(2	ext{ heads}) = \frac{3}{8}$$

Question 16

Which of the following statements about the mean and median is true for a symmetric distribution?

Accepted Answer

The mean and median are equal.

Question 17

A data set has a mean of $$50$$ and a standard deviation of $$5. $$What is the $$z-$$score for a value of $$40$$?

Accepted Answer

$$z = \frac{40 - 50}{5} = -2$$

Question 18

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is always less than the mean.

Question 19

If a data set has a five-number summary: Min = 2, Q1 = 4, Median = 7, Q3 = 10, Max = 15, what is the range and interquartile range (IQR)?

Accepted Answer

Range = $$15 - 2 = 13$$, IQR = $$10 - 4 = 6$$

Statistics Study Notes: Descriptive Statistics, Data Visualization, and Probability

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