SOLUTION: If the mean height of bonsai trees is 52 cm with a standard deviation of 10 cm, 95% of the trees are between _________ and _________. -62 -82 -32 -42 -22 -72

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Question 1202985: If the mean height of bonsai trees is 52 cm with a standard deviation of 10 cm, 95% of the trees are between _________ and _________.

-62
-82
-32
-42
-22
-72
Answer by math_tutor2020(3817) About Me  (Show Source):
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Answer: 95% of the trees are between    32 cm    and    72 cm   

Explanation:

The Empirical Rule says that roughly 95% of the normally distributed population is within 2 standard deviations of the mean.

Subtract off 2 copies of the standard deviation from the mean.
mean - 2*standardDev = 52 - 2*10 = 32
That's the lower boundary.

Then add 2 copies of the standard deviation to the mean.
mean + 2*standardDev = 52 + 2*10 = 72
That's the upper boundary.

We can say P(32 < x < 72) = 0.95 approximately.
In other words, the area under this particular normal distribution curve between x = 32 and x = 72 is roughly 0.95