Q: In a study of e-commerce purchases, suppose the probability that a visitor makes a purchase is $p = 0.2$. Out of 15 visitors, what is the expected number of purchases?

$ E(X) = np = 15 \times 0.2 = 3 $

Q: Suppose you want to compute the sample covariance between two variables $X$ and $Y$ with $n$ observations. Which formula should you use?

$ S_{XY} = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y}) $

Q: If the sample correlation coefficient between two variables is $r = 0.85$, what does this indicate about the relationship between the variables?

There is a strong positive linear relationship.

Q: Suppose you are analyzing the relationship between Year and March Arctic Sea Ice Extent. If the correlation coefficient is negative, what does this imply?

As the year increases, the March sea ice extent decreases.

Q: If a distribution is binomial with $p = 0.5$ and $n = 100$, what is the expected shape of the distribution?

Approximately symmetric and bell-shaped (normal).

Question 1

Standard & Poor (S&P) provides ratings for the creditworthiness of countries using a letter scale from AAA (highest) to D (lowest). What type of data is represented by these ratings?

Accepted Answer

Qualitative, because the ratings are categorical labels.

Question 2

Given the S&P ratings table, what is the level of measurement for the ratings data?

Accepted Answer

Ordinal, because the ratings have a meaningful order.

Question 3

A hotel asks customers to rate their stays as Excellent, Good, Fair, or Poor. If 105 men and 31.5 women rated their stay as Excellent, what is the probability that a randomly selected customer rated their stay as Excellent? (Total customers: 105 + 70 + 56 + 21 + 31.5 + 42 + 24.5 + 7)

Accepted Answer

$ \frac{105 + 31.5}{105 + 70 + 56 + 21 + 31.5 + 42 + 24.5 + 7} $

Question 4

Suppose the probability that a customer rates their stay as Excellent is $0.25$. If 15 customers are surveyed, what is the probability that exactly 4 rate their stay as Excellent? Use the binomial formula.

Accepted Answer

$ \binom{15}{4} (0.25)^4 (0.75)^{11} $

Question 5

A random variable $X$ follows a normal distribution with $\mu = 124$ and $\sigma = 27$. What is the probability that a randomly selected value is between 120 and 140?

Accepted Answer

Find $z$-scores: $z_1 = \frac{120 - 124}{27}$, $z_2 = \frac{140 - 124}{27}$, then $P(120 < X < 140) = P(z_1 < Z < z_2)$

Question 6

In a study of e-commerce purchases, suppose the probability that a visitor makes a purchase is $p = 0.2$. Out of 15 visitors, what is the expected number of purchases?

Accepted Answer

$ E(X) = np = 15 	imes 0.2 = 3 $

Question 7

Suppose you want to compute the sample covariance between two variables $X$ and $Y$ with $n$ observations. Which formula should you use?

Accepted Answer

$ S_{XY} = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y}) $

Question 8

If the sample correlation coefficient between two variables is $r = 0.85$, what does this indicate about the relationship between the variables?

Accepted Answer

There is a strong positive linear relationship.

Question 9

Arctic Sea Ice Extent is decreasing at a rate of about 12.2% per decade due to climate change. If the extent was 10 million square kilometers in 1990, what is the expected extent in 2020?

Accepted Answer

$ 10 	imes (1 - 0.122)^{3} $

Question 10

A random variable $X$ follows a normal distribution with $\mu = 124$ and $\sigma = 27$. What is the $z$-score for $X = 180$?

Accepted Answer

$ z = \frac{180 - 124}{27} $

Question 11

Suppose you are analyzing the relationship between Year and March Arctic Sea Ice Extent. If the correlation coefficient is negative, what does this imply?

Accepted Answer

As the year increases, the March sea ice extent decreases.

Question 12

A hotel survey shows that 70 men and 42 women rated their stay as Good. What is the probability that a randomly selected customer was a woman, given that they rated their stay as Good?

Accepted Answer

$ \frac{42}{70 + 42} $

Question 13

If a distribution is binomial with $p = 0.5$ and $n = 100$, what is the expected shape of the distribution?

Accepted Answer

Approximately symmetric and bell-shaped (normal).

Question 14

Suppose the sample covariance between $X$ and $Y$ is zero. What does this tell you about the relationship between $X$ and $Y$?

Accepted Answer

There is no linear relationship between $X$ and $Y$.

Question 15

A random variable $X$ follows a normal distribution with $\mu = 124$ and $\sigma = 27$. What is the probability that $X$ is greater than 180?

Accepted Answer

Find $z = \frac{180 - 124}{27}$, then $P(X > 180) = 1 - P(Z < z)$

Question 16

In a binomial experiment with $n = 15$ and $p = 0.2$, what is the variance of the number of successes?

Accepted Answer

$ 	ext{Var}(X) = np(1-p) = 15 	imes 0.2 	imes 0.8 $

Question 17

If the probability that a customer makes a purchase is $0.2$, what is the probability that none of 5 customers make a purchase?

Accepted Answer

$ (1 - 0.2)^5 $

Question 18

A hotel survey shows that 21 men and 7 women rated their stay as Poor. What is the probability that a randomly selected customer was a woman, given that they rated their stay as Poor?

Accepted Answer

$ \frac{7}{21 + 7} $

Statistics for Business: Quiz Study Guide (Chapters 1-6)

Study Guide - Practice Questions

Study Guide - Flashcards