Algebra 2 The Normal Distribution Test with Point Values (PDF)

Algebra 2 math test: The Normal Distribution – Maths PDF

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This algebra 2 normal distribution test for Algebra 2 covers the normal distribution (Common Core S-ID.A.4), with a free PDF to print.

This 45-minute test on the normal distribution has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: The Normal Distribution
Standards: S-ID.A.4
Time: 45 minutes
Total: 20 points

Algebra 2 normal distribution test: questions

Question 1 – Empirical rule [2 pts]

IQ-style scores.

Scores are approximately normal with mean 100 and standard deviation 15. What percent are between 85 and 115? What percent are between 70 and 130?

Question 2 – z-score [2 pts]

A runner’s time of 24 minutes is in a race with mean 30 minutes and standard deviation 4 minutes. Find the z-score and interpret it.

Question 3 – Compare [3 pts]

Aisha scored 91 on a test with mean 80 and standard deviation 5. Ethan scored 96 on a test with mean 85 and standard deviation 8. Who scored higher relative to the class?

Question 4 – Area between [3 pts]

Standard normal curve.

Use a standard normal table or calculator to find the proportion of a normal distribution between \(z = -1.5\) and \(z = 1\).

Question 5 – Percent above [2 pts]

Heights are normal with mean 64 inches and standard deviation 2.5 inches. What percent are taller than 69 inches?

Question 6 – Find the value [2 pts]

Scores have mean 500 and standard deviation 80. What score has z-score -0.5?

Question 7 – Count [2 pts]

Weights of packages in ounces.

Package weights are normal with mean 70 ounces and standard deviation 4 ounces. About how many of 500 packages weigh more than 78 ounces?

Question 8 – Percentile [2 pts]

The 80th percentile has z-score about 0.84. For scores with mean 60 and standard deviation 10, find the 80th percentile score.

Question 9 – Find the error [2 pts]

Liam says that in a normal distribution about 95% of data are within 1 standard deviation of the mean. Correct him and give the percent for 1 standard deviation.

Key facts behind this algebra 2 normal distribution test

Key facts

Normal distribution: symmetric, bell-shaped, described by its mean and standard deviation.
68-95-99.7 rule for 1, 2, 3 standard deviations.
z = (x – mean) / sd and x = mean + z times sd.
Area under the curve = proportion of data.
Compare different distributions with z-scores.

How to use this algebra 2 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 Algebra 2 chapters: Algebra 2 math.

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