Q: A bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is not blue?

$$P(\text{not blue}) = \frac{7}{10}$$

Q: Which formula would you use to find the probability of both events E and F occurring, if E and F are independent?

$$P(E \text{ and } F) = P(E) \times P(F)$$

Q: A random variable X represents the number of heads in 4 flips of a fair coin. What is the probability of getting exactly 2 heads?

$$P(X=2) = \binom{4}{2} (0.5)^2$ (0.5)^2$ = 6 \times 0.25 \times 0.25 = 0.375$$

Question 1

Which of the following best describes a variable measured as 'the brand of cereal a person eats for breakfast'?

Accepted Answer

A qualitative, categorical variable

Question 2

A researcher wants to estimate the average height of all university students. She randomly selects 100 students and calculates their average height. In this context, what is the average height of the 100 students called?

Accepted Answer

A statistic

Question 3

Which sampling method involves dividing the population into groups based on a shared characteristic and then randomly selecting some groups to include all their members in the sample?

Accepted Answer

Cluster sampling

Question 4

A histogram is different from a bar graph because:

Accepted Answer

The bars in a histogram touch each other, representing continuous data

Question 5

Given the data set: 10, 12, 14, 16, 18, what is the range?

Accepted Answer

$$	ext{Range} = 18 - 10 = 8$$

Question 6

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

$$95\%$$

Question 7

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 8

Which of the following is NOT a characteristic of a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial

Question 9

If $$P(E) = 0.3$$ and $$P(F) = 0.2$$ and E and F are disjoint, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$P(E 	ext{ or } F) = 0.5$$

Question 10

A bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is not blue?

Accepted Answer

$$P(	ext{not blue}) = \frac{7}{10}$$

Question 11

Which formula would you use to find the probability of both events E and F occurring, if E and F are independent?

Accepted Answer

$$P(E 	ext{ and } F) = P(E) 	imes P(F)$$

Question 12

How many ways can a committee of 3 be chosen from 8 people?

Accepted Answer

$$\binom{8}{3} = 56$$

Question 13

A random variable X represents the number of heads in 4 flips of a fair coin. What is the probability of getting exactly 2 heads?

Accepted Answer

$$P(X=2) = \binom{4}{2} (0.5)^2$ (0.5)^2$ = 6 	imes 0.25 	imes 0.25 = 0.375$$

Question 14

If a distribution is right-skewed, which of the following is true?

Accepted Answer

Mean \u003e Median

Question 15

Which of the following is the correct formula for the standard deviation of a binomial distribution?

Accepted Answer

$$\sigma = \sqrt{npq}$$

Question 16

A percentile rank is calculated using which formula for the kth percentile in a data set of n values?

Accepted Answer

$$i = \frac{k(n+1)}{100}$$

Question 17

Which of the following is an example of a continuous random variable?

Accepted Answer

The time it takes to run a marathon

Question 18

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$P(A 	ext{ or } B) = 0.9$$

Introductory Statistics Midterm Review Study Guide

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