AP Stats Normal Distribution and Z-Scores

Question 1

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

Accepted Answer

It has a finite range determined by the minimum and maximum values.

Answer

The normal distribution extends from negative infinity to positive infinity, so it does not have a finite range.

Question 2

A standardized test has scores that follow a normal distribution with mean 500 and standard deviation 100. What is the z-score for a student who scored 650?

Accepted Answer

1.5

Answer

z = (650 - 500) / 100 = 150 / 100 = 1.5.

Question 3

According to the Empirical Rule, approximately what percentage of data in a normal distribution falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

The Empirical Rule states that approximately 68% of data falls within one standard deviation of the mean in a normal distribution.

Question 4

A normal distribution has mean μ = 40 and standard deviation σ = 5. What value corresponds to z = -2?

Accepted Answer

30

Answer

x = μ + zσ = 40 + (-2)(5) = 40 - 10 = 30.

Question 5

Which of the following describes a z-score of -1.8?

Accepted Answer

The value is 1.8 standard deviations below the mean.

Answer

A negative z-score indicates the value is below the mean, and the magnitude (1.8) tells us how many standard deviations below.

AP Practice Test

AP Practice Test

AP Stats Normal Distribution and Z-Scores