Question 1

Which of the following is NOT a property of a normal distribution?

Accepted Answer

The curve is skewed to the right.

Question 2

A normal distribution is defined as a continuous probability distribution for a random variable $$x. $$Which of the following statements best describes the shape of its graph?

Accepted Answer

It is bell-shaped and symmetric about the mean.

Question 3

If the mean of a normal distribution is 600 and the standard deviation is 20, what percentage of values falls between 560 and 640 according to the Empirical Rule?

Accepted Answer

About 95%

Question 4

Which formula is used to convert an $$x-$$value to a $$z-$$score in a normal distribution?

Accepted Answer

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

Question 5

Which of the following is a requirement for a probability density function (pdf) of a continuous random variable?

Accepted Answer

The total area under the curve must be equal to 1.

Question 6

A standard normal distribution has which of the following characteristics?

Accepted Answer

Mean of 0 and standard deviation of 1.

Question 7

If the area to the left of $$z = 1.15 is 0.8749$$, what is the area to the right of $$z = 1.15$$?

Accepted Answer

0.1251

Question 8

Which statement about the inflection points of a normal curve is correct?

Accepted Answer

They occur at $$\mu \pm \sigma.$$

Question 9

A student scores 620 on a test with a mean of 600 and a standard deviation of 20. What is the student's $$z-$$score?

Accepted Answer

$$z = \frac{620 - 600}{20} = 1$$

Question 10

Which of the following best describes the cumulative area under the standard normal curve for $$z = 0$$?

Accepted Answer

0.5000

Question 11

If you want to find the area between $$z = 0.5$$ and $$z = 1.2$$, which steps should you follow?

Accepted Answer

Find the area for $$z = 0.5$$ and $$z = 1.2$$ and subtract the smaller from the larger.

Question 12

Which real-world scenario is most likely to be modeled by a normal distribution?

Accepted Answer

The heights of adult humans in a population.

Question 13

If a normal distribution has a mean of 50 and a standard deviation of 5, which curve would be more spread out: one with $$\sigma = 5 or $$one with $$\sigma = 10$$?

Accepted Answer

The curve with $$\sigma = 10.$$

Question 14

Which of the following statements is TRUE about the area under the normal curve?

Accepted Answer

The area under the curve is always equal to 1.

Question 15

A hospital records the time (in minutes) patients spend waiting for a doctor. If this time is modeled by a normal distribution, which property must the distribution have?

Accepted Answer

The mean, median, and mode are all equal.

Question 16

If the cumulative area for $$z = 3.49 is $$close to 1, what does this imply about the probability of observing a value greater than $$z = 3.49$$?

Accepted Answer

It is close to 0.

Question 17

Which of the following is NOT a requirement for a probability density function (pdf)?

Accepted Answer

The function must be defined for all real numbers.

Question 18

A researcher wants to find the probability that a randomly selected value from a normal distribution is greater than a certain $$z-$$score. Which method should they use?

Accepted Answer

Find the area to the left of the $$z-$$score and subtract it from 1.

Question 19

Which of the following best describes the relationship between the mean and the line of symmetry in a normal distribution?

Accepted Answer

The mean is located at the line of symmetry.

Normal Probability Distributions: Study Notes for Statistics Students

Study Guide - Practice Questions

Study Guide - Flashcards