AP Stats Normal Distribution and Z-Scores 2

Question 1

Heights of adult women are approximately normal with mean 64 inches and standard deviation 2.5 inches. What percentage of women are shorter than 69 inches?

Accepted Answer

97.72%

Answer

z = (69 - 64) / 2.5 = 2.0; P(Z < 2) ≈ 0.9772, or 97.72%.

Question 2

Which of the following z-scores corresponds to the 84th percentile of a standard normal distribution?

Accepted Answer

1.00

Answer

P(Z < 1.00) ≈ 0.8413, which is approximately the 84th percentile.

Question 3

A normal distribution has the property that the area to the left of z = 1.28 is approximately 0.90. What percentile does z = 1.28 represent?

Accepted Answer

90th

Answer

If the area to the left is 0.90, then z = 1.28 corresponds to the 90th percentile.

Question 4

Two normal distributions have the same mean but different standard deviations. Which statement is true?

Accepted Answer

The distribution with the smaller standard deviation is taller and narrower.

Answer

A smaller standard deviation means data is more concentrated near the mean, producing a taller and narrower bell curve.

Question 5

A student's AP exam score has a z-score of 2.3. What does this indicate?

Accepted Answer

The score is 2.3 standard deviations above the mean.

Answer

A z-score measures the number of standard deviations a value is from the mean; z = 2.3 means 2.3 standard deviations above.

AP Practice Test

AP Practice Test

AP Stats Normal Distribution and Z-Scores 2