Algebra 2 Practice Test: Normal Distribution
- Normal Distribution
- 10 questions
- 15 minutes
These 10 questions practice the empirical rule (68-95-99.7), z-scores and the shape of normal curves. About 68% of the data lie within 1 standard deviation of the mean, about 95% within 2 and about 99.7% within 3, and the curve is symmetric, so each half holds 50%.
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Question 1
Adult heights in a group are normally distributed with mean 64 inches and standard deviation 2.5 inches. About what percent of the group is between 61.5 and 66.5 inches tall?
Correct answer: C
61.5 and 66.5 are 1 standard deviation below and above the mean (64 ± 2.5), and about 68% of the data lie within 1 standard deviation. 34% is only one half of that interval.
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Question 2
Scores on an exam are normally distributed with mean 500 and standard deviation 100. About what percent of scores are above 700?
Correct answer: D
700 is 2 standard deviations above the mean. About 95% lie within 2 standard deviations, so 5% lie outside, half on each side: 2.5%.
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Question 3
Which statement is true for every normal distribution?
Correct answer: C
A normal curve is symmetric with one peak, so the mean, median and mode are all at the center. Its standard deviation can be any positive number, and 95% belongs to 2 standard deviations.
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Question 4
A data set is normally distributed with mean 80 and standard deviation 6. Which value has a z-score of −1.5?
Correct answer: B
x = mean + z · SD = 80 + (−1.5)(6) = 80 − 9 = 71. Subtracting only 1.5 gives 78.5, and using the wrong sign gives 89.
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Question 5
Ana scored 82 on a test with mean 70 and standard deviation 6. Ben scored 90 on a different test with mean 80 and standard deviation 8. Which statement is correct?
Correct answer: A
Ana: z = (82 − 70)/6 = 2. Ben: z = (90 − 80)/8 = 1.25. A higher z-score means a better position within the group, so Ana did better even though her raw score is lower.
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Question 6
In a normal distribution, about what percent of the data lie more than 1 standard deviation below the mean?
Correct answer: B
About 68% lie within 1 standard deviation, so 32% lie outside, split equally: 16% below and 16% above. 32% counts both tails.
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Question 7
A machine fills 400 bags of rice. The weights are normally distributed with mean 16 ounces and standard deviation 0.2 ounce. About how many bags weigh between 15.6 and 16.4 ounces?
Correct answer: A
15.6 and 16.4 are 2 standard deviations from the mean, so about 95% of the bags are in this range: 0.95 · 400 = 380. 272 uses 68%, which belongs to 1 standard deviation.
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Question 8
A normal distribution has mean 50 and standard deviation 4. Which interval contains about the middle 99.7% of the data?
Correct answer: D
99.7% lie within 3 standard deviations: 50 ± 3 · 4 = 50 ± 12, so 38 to 62. 42 to 58 is the 95% interval.
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Question 9
Two normal curves have the same mean. Curve P has standard deviation 5 and curve Q has standard deviation 10. How do they compare?
Correct answer: B
A larger standard deviation spreads the data out, so the curve is wider. The total area stays 1, so a wider curve must have a lower peak. The mean, not the standard deviation, sets the center.
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Question 10
In a normal distribution, about what percent of the data lie between the mean and 2 standard deviations above the mean?
Correct answer: A
About 95% lie within 2 standard deviations on both sides together, and the curve is symmetric, so one side holds half: 47.5%. 13.5% is only the part between 1 and 2 standard deviations.
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