Q: A password consists of 2 letters followed by 3 digits. If letters and digits can be repeated, how many possible passwords are there? Use the multiplication rule.

$$ 26^2$ \times 10^3$ = 676,000 $$

Question 1

A researcher wants to study the effect of a new drug on blood pressure. She collects data on patients' blood pressure before and after taking the drug. Which level of measurement best describes the blood pressure readings?

Accepted Answer

Ratio

Question 2

Which of the following variables is both quantitative and continuous?

Accepted Answer

Temperature measured in degrees Celsius

Question 3

A set of exam scores is: 55, 60, 65, 70, 95. Which measure of central tendency is most resistant to the outlier?

Accepted Answer

Median

Question 4

Given the data set: 2, 4, 6, 8, 10, what is the sample standard deviation? Use the formula $$ s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}} .$$

Accepted Answer

$$ s = 2.83 $$

Question 5

A student receives the following grades: Homework (80, weight 1), Midterm (90, weight 2), Final (85, weight 3). What is the weighted mean of the grades? Use $$ \bar{x} = \frac{\sum w_i x_i}{\sum w_i} .$$

Accepted Answer

$$ 85.83 $$

Question 6

A boxplot of cholesterol levels in adults shows a long whisker on the right and several points beyond the upper fence. What does this indicate about the data?

Accepted Answer

There are outliers and the data are right-skewed.

Question 7

If the mean of a data set is 50 and the standard deviation is 5, what is the z-score for a value of 60? Use $$ z = \frac{x - 	ext{mean}}{	ext{std dev}} .$$

Accepted Answer

$$ z = 2 $$

Question 8

A survey finds that the 90th percentile of annual income in a city is $120,000. What does this mean?

Accepted Answer

90% of people earn less than $120,000.

Question 9

Given Q₁ = 20, Q₃ = 40, and the following data point: 5, is this point an outlier? Use the lower fence formula $$ 	ext{Lower Fence} = Q_1$ - 1.5 	imes IQR .$$

Accepted Answer

Yes, because 5 is below the lower fence.

Question 10

A bag contains 3 red, 5 blue, and 2 green marbles. What is the classical probability of randomly selecting a blue marble? Use $$ P(E) = \frac{	ext{number of ways E can occur}}{	ext{total outcomes}} .$$

Accepted Answer

$$ 0.4 $$

Question 11

If the probability of owning a cat is 0.3, what is the probability of not owning a cat? Use the complement rule $$ P(E^C) = 1 - P(E) .$$

Accepted Answer

$$ 0.7 $$

Question 12

In a group of 50 students, 20 play tennis, 15 play soccer, and 5 play both. What is the probability that a randomly selected student plays tennis or soccer? Use $$ P(E 	ext{ or } F) = P(E) + P(F) - P(E 	ext{ and } F) .$$

Accepted Answer

$$ 0.6 $$

Question 13

A fair coin is flipped and a fair die is rolled. What is the probability of getting heads and a 6? Use $$ P(E 	ext{ and } F) = P(E) 	imes P(F) .$$

Accepted Answer

$$ \frac{1}{12} $$

Question 14

If P(A and B) = 0.15 and P(B) = 0.5, what is the conditional probability P(A|B)? Use $$ P(A|B) = \frac{P(A 	ext{ and } B)}{P(B)} .$$

Accepted Answer

$$ 0.3 $$

Question 15

How many ways can 4 different books be arranged on a shelf? Use the formula $$ n! .$$

Accepted Answer

$$ 24 $$

Question 16

A committee of 3 is to be chosen from 8 people. How many different committees are possible? Use $$ nC_r = \frac{n!}{r!(n - r)!} .$$

Accepted Answer

$$ 56 $$

Question 17

A password consists of 2 letters followed by 3 digits. If letters and digits can be repeated, how many possible passwords are there? Use the multiplication rule.

Accepted Answer

$$ 26^2$ 	imes 10^3$ = 676,000 $$

Question 18

A simulation is used to estimate the probability of a rare event in a chemical reaction. Why might simulation be preferred over theoretical calculation?

Accepted Answer

Because the theoretical probability is difficult or impossible to compute.

Question 19

A hospital reports that the probability a patient recovers from a surgery is 0.95. What is the probability that at least one out of two patients does NOT recover? Use $$ P(	ext{at least one fails}) = 1 - P(	ext{both recover}) .$$

Accepted Answer

$$ 0.0975 $$

Statistics Study Guide: Data Collection, Summarizing Data, and Probability

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