Question 1

Which of the following best defines a point estimate?

Accepted Answer

A single value used to approximate a population parameter.

Question 2

A random variable $$X$$ represents the number of cars passing through a toll booth in an hour. Is $$X$$ discrete or continuous?

Accepted Answer

Discrete, because the number of cars can only take whole number values.

Question 3

Which of the following is NOT a requirement for a probability distribution?

Accepted Answer

The mean must be equal to the median.

Question 4

Which symbol in the confidence interval formula represents the sample proportion?

Accepted Answer

$$\hat{p}$$

Question 5

Under what condition would a $$z-$$score be negative?

Accepted Answer

When the data value is less than the mean.

Question 6

Which of the following is a correct interpretation of a 99% confidence interval $$4.1 \u003c \mu \u003c 5.6$$?

Accepted Answer

We are 99% confident that the population mean $$\mu is $$between 4.1 and 5.6.

Question 7

Which of the following is a biased estimator?

Accepted Answer

Sample range

Question 8

If you are asked to find the 85th percentile in a normal distribution, you are being asked to find:

Accepted Answer

The value below which 85% of the data falls.

Question 9

Which of the following groups contains terms that can be used interchangeably?

Accepted Answer

Mean, expected value, population average

Question 10

Which of the following does NOT describe the standard normal distribution?

Accepted Answer

It has a mean of 1.

Question 11

Which formula gives the standard deviation $$\sigma$$ for a binomial distribution with parameters $$n$$ and $$p$$?

Accepted Answer

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

Question 12

Suppose you want to find the probability that a standard normal random variable $$z is $$greater than 1.5. Which of the following steps is correct?

Accepted Answer

Find the area to the right of $$z = 1.5$$ using the standard normal table.

Question 13

Which of the following best describes the Central Limit Theorem?

Accepted Answer

The sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 14

A random variable $$Y$$ represents the amount of rainfall in a city in a day (in inches). Is $$Y$$ discrete or continuous?

Accepted Answer

Continuous, because rainfall can take any value within a range.

Question 15

Which of the following is the formula for the mean $$\mu of a $$binomial distribution with parameters $$n$$ and $$p$$?

Accepted Answer

$$\mu = np$$

Question 16

A hospital tests 10 generators and records whether each one fails to operate. What is the probability that at least one generator fails, if the probability that a generator works is 0.98?

Accepted Answer

$$1 - (0.98$$)^{10}$$

Question 17

Which of the following best defines a density curve?

Accepted Answer

A curve that describes the overall pattern of a distribution and has total area equal to 1.

Question 18

The symbols $$z_{\alpha/2}$$ and $$t_{\alpha/2} in $$confidence interval formulas are called:

Accepted Answer

Critical values

Question 19

A researcher flips a coin 20 times and records the number of heads. Does this procedure result in a binomial distribution?

Accepted Answer

Yes, because each flip is independent and has two possible outcomes.

Question 20

Suppose you have a normal distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the $$z-$$score for a value $$x = 130$$?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2$$

Step-by-Step Guidance for Statistics Exam Review (Chapters 5–7)

Study Guide - Practice Questions

Study Guide - Flashcards