AP Statistics z-Scores and the Normal Distribution Test with Point Values (PDF)

AP Statistics math test: z-Scores and the Normal Distribution – Maths PDF

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This ap statistics normal distribution test for AP Statistics covers z-scores and the normal distribution (Common Core AP STAT 1.10, AP STAT 1.11, HSS-ID.A.4), with a free PDF to print.

This 45-minute test covers z-scores, the empirical rule, normal probabilities, and percentiles. Draw a shaded sketch for each probability, show the standardizing step, and state conclusions in context.

Time and points

About this test

Grade: AP Statistics
Chapter: z-Scores and the Normal Distribution
Standards: AP STAT 1.10, AP STAT 1.11, HSS-ID.A.4
Time: 45 minutes
Total: 20 points

Ap statistics normal distribution test: questions

Question 1 – z-scores [3 pts]

Test scores are normal with mean 70 and standard deviation 10. (a) Find the z-score of 88. (1 point) (b) Find the score with z = -0.5. (1 point) (c) Interpret z in (a). (1 point)

Question 2 – Normal area [3 pts]

Test scores.

Find the proportion of scores between 60 and 90. (3 points)

Question 3 – Empirical rule [2 pts]

Daily visitors.

Daily visitors are approximately normal with mean 500 and standard deviation 50. Use the empirical rule to find the percent of days with more than 600 visitors.

Question 4 – Percentile [3 pts]

Find the score at the 80th percentile for the test-score distribution (mean 70, sd 10). Interpret it. (3 points)

Question 5 – Compare scores [2 pts]

Priya scored 1,180 on a test with mean 1,050 and sd 100. Diego scored 27 on a test with mean 21 and sd 4.5. Who did relatively better?

Question 6 – Counts from the rule [2 pts]

Bottle volume.

Of 800 bottles in a day (volumes normal with mean 12 oz and sd 0.15 oz), about how many have between 11.85 and 12.15 oz?

Question 7 – Rejection rate [3 pts]

Bottle volume.

Bottle volumes are normal with mean 12 oz and sd 0.15 oz. Find the proportion with less than 11.8 oz. (3 points)

Question 8 – Unit change [2 pts]

Weights in pounds have mean 150 and sd 20. Find the mean and sd in kilograms (1 lb = 0.4536 kg). Does a z-score change?

Key facts behind this ap statistics normal distribution test

Key facts

z = (x – mean) / sd measures position in standard deviations.
Empirical rule: 68% within 1 sd, 95% within 2 sd, 99.7% within 3 sd.
Area under the curve over an interval is the proportion of values in it; total area is 1.
Use normalcdf for areas and invNorm for percentiles; always sketch and shade first.
A percentile is the percent of values at or below a given value.

How to use this ap statistics normal distribution test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

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