, and
. The percentages given here don't add to 100% because they are
rounded. |
Approximately 68% of the population will lie within one standard deviation of the mean. The percentages are based on the area under the curve. Note that about 68% of the area under the curve is within 2 standard deviations of the mean.
About 95% of the population will be within 2 standard deviations of the mean. Approximately 2% of the area under the curve lies between 2 and 3 standard deviations either side of the mean. Over 99% will be within 3 standard deviations of the mean. Only 0.2% of the area under the normal curve lies outside 3 standard deviations from the mean. |
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One study showed that gasoline use for "compact" cars sold in
the US is normally distributed with an average of 25.5 mpg. The
standard deviation is 4.5 mpg. We can be pretty sure that: About 68% got between 21 and 30 mpg since 25.5 – 4.5 = 21 and 25.5 + 4.5 = 30. About 95% of all compacts got mileages between 16.5 and 34.5 mpg since 25.5 – 2(4.5) =16.5 and 25.5 + 2(4.5) = 34.5 About 99% got between 12 and 39 mpg since 25.5 – 3(4.5) = 16.5 and 25.5 + 3(4.5) = 39 #21 Write in the remaining miles per gallon corresponding to the standard deviation intervals as calculated above. This kind of information would be useful for energy planning. |
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#22 Assume the average height of men is 69 inches and the standard
deviation is 3 inches. About what percentage of men will have
a height between 69 and 72 inches? ________
It will help to label the standard deviation intervals with their corresponding heights. #23 What height range will contain 99% of all men? #24 Choosing at random, how likely is it to find a man taller than 6'-6" ? _____________________ |
#24.2 A student collects data on beer prices to produce the chart at
left. The student claims beer prices are approximately normally
distributed.
How would you respond?
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