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

It is symmetric about the mean.

Answer

The mean, median, and mode are all equal.

Answer

Approximately 95% of data falls within 2 standard deviations of the mean.

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

1.0

Answer

2.0

Answer

0.65

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

50%

Answer

95%

Answer

99.7%

Question 4

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

Accepted Answer

30

Answer

35

Answer

45

Answer

50

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

The value is 1.8 standard deviations above the mean.

Answer

The value is 1.8 units below the mean.

Answer

The value is in the 1.8th percentile.

Question 6

A class has test scores normally distributed with mean 75 and standard deviation 8. What is the probability that a randomly selected student scored above 83?

Accepted Answer

0.1587

Answer

0.3413

Answer

0.8413

Answer

0.6826

Question 7

If X is normally distributed with μ = 60 and σ = 12, which of the following is the area under the normal curve between x = 48 and x = 72?

Accepted Answer

0.6826

Answer

0.50

Answer

0.3413

Answer

0.9544