8
QuizMultiple Choice

Introduction to Normal Distributions — Quiz

Question 8 • Mathematics III

The heights of a certain type of tree are approximately normally distributed with a mean height mu is equal to 5 ft and a standard deviation sigma is equal to 0 point 4 ft. Which statement must be true?

Answer
A
A tree with a height of 6 point 2 ft is 3 standard deviations above the mean.
B
A tree with a height of 4 point 6 ft is 1 standard deviation above the mean.
C
A tree with a height of 5 point 4 ft is 1 standard deviation below the mean.
D
A tree with a height of 5 point 8 ft is 2 point 5 standard deviations above the mean.

Explanation

To find how many standard deviations a height is from the mean, subtract the mean height, 5 ft, and divide by the standard deviation, 0.4 ft. For a height of 6.2 ft, (6.2 − 5) ÷ 0.4 = 3, so it is 3 standard deviations above the mean. The statement that a 6.2-ft tree is 3 standard deviations above the mean is correct.

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