Question 1

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that cannot occur at the same time.

Question 2

A random variable $$X$$ has the following probability distribution:

$$\begin{array}{c|c}
X & P(X) \
\hline
1 & 0.1 \
2 & 0.3 \
3 & 0.4 \
4 & 0.2 \
\end{array}$$

What is the expected value $$E[X]$$?

Accepted Answer

$$E[X] = 2.7$$

Question 3

True or False: If an event has a probability of $$0.9999$$, then it is guaranteed to occur.

Accepted Answer

False

Question 4

Which of the following is the formula for the standard deviation of a binomial random variable with parameters $$n$$ and $$p$$?

Accepted Answer

$$\sqrt{np(1-p)}$$

Question 5

You have a bowl with 150 M&Ms: 72 plain and 78 peanut. There are 41 yellow M&Ms in total. What is the probability that a randomly selected M&M is yellow?

Accepted Answer

$$\frac{41}{150}$$

Question 6

True or False: Mutually exclusive events are also independent.

Accepted Answer

False

Question 7

For a standard normal distribution, what percentage of observations fall between $$-2$$ and $$2$$ according to the Empirical Rule?

Accepted Answer

Approximately 95%

Question 8

As the sample size increases, what happens to the width of the confidence interval for the mean?

Accepted Answer

It decreases.

Question 9

Suppose the mean number of cakes sold per week at 47 bakeries is 31.2 with a population standard deviation of 7.1. What is the 95% confidence interval for the population mean number of cakes sold per week? (Use $$z^* = 1.96)$$

Accepted Answer

$$31.2 \pm 2.03$$

Question 10

A survey found that 38% of Americans favor dogs over cats. If 50 Americans are randomly selected, what is the expected number of Americans who favor dogs?

Accepted Answer

$$19$$

Question 11

Which of the following is the formula for a $$z-$$score for a sample mean $$\bar{x}$$, population mean $$\mu$$, and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\sigma}$$

Question 12

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 13

A QQ-plot is used to:

Accepted Answer

Visually assess whether data are from a normal distribution.

Question 14

If the confidence level decreases, what happens to the width of the confidence interval?

Accepted Answer

It decreases.

Question 15

In a normal distribution, what is the maximum number of acres burned to be considered a 'good year' if good years are the lowest 5% of the years? (Assume mean $$\mu$$ and standard deviation $$\sigma$$ are known.)

Accepted Answer

$$\mu - 1.645\sigma$$

Question 16

Which of the following is NOT a property of a discrete random variable?

Accepted Answer

It can take on an infinite number of values within an interval.

Question 17

If $$P(A) = 0.7$$, what is the probability of the complement of $$A$$?

Accepted Answer

$$0.3$$

Question 18

A sample of size $$n = 50$$ has a mean $$\bar{x} = 680. $$What is the standardized version (z-score) of this sample if the population mean is $$\mu = 650$$ and $$\sigma = 40$$?

Accepted Answer

$$z = \frac{680 - 650}{40/\sqrt{50}}$$

Question 19

In a survey of 93 young adults, the mean age for first driving a car is 16.8 years with a standard deviation of 3.1 years. What is the point estimate for the population mean age?

Accepted Answer

$$16.8$$

Statistics Exam 2 Review: Probability, Distributions, and Confidence Intervals

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