Question 1141014
<b>​(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 26 inches from 16 ​inches?</b>
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It is five standard deviations away.  This is because 26 inches is 10 inches away from 16 inches, and 10 divided by 2 (which is one standard deviation) is 5.
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<b>​(b) Is 26 inches far away from a mean of 16 ​inches?</b>
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With a standard deviation of 2, it is VERY far away.  (See above...FIVE standard deviations away.)  Less than 0.1% of all values would be expected to exceed 26 inches.
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<b>(c) Suppose the standard deviation of the underlying data is 8 inches. Is 26 inches far away from a mean of 16 ​inches?</b>
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With a standard deviation of 8 inches, a value of 26 inches is 1.25 standard deviations away.  (26 inches is 10 inches away from 16 inches, and 10 divided by 8 is 1.25.)
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With a standard deviation of 8, about 10% of values would be expected to exceed 26 inches.  Furthermore, with a standard deviation of 8, about 80% of the values would be expected to fall between 6 and 26 inches.