b) 1, 3, 5, 4, 3, 20
The Empirical Rule: (Also known as the “Three Sigma Rule”)
When a population has a histogram that is roughly bell-shaped, then
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•
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approximately 68% of the data will be within 1 standard deviation from the mean.
approximately 95% of the data will be within 2 standard deviations from the mean.
all or almost all of the data will be within 3 standard deviations from the mean.
Example: The GMAC Insurance company reported that the mean score on the 2009 National Drivers
Test was 76.6, with a standard deviation of 2.7 points. The test scores are approximately bell-shaped.
Estimate the percent of participants in the test who had scores between
a) 68.5 and 84.7
b) 73.9 and 79.3
c) Between what two values will approximately 95% of the scores
be?
Example: A certain type of bolt used in an aircraft must have a
length between 122 and 128 millimeters in order to be acceptable.
The manufacturing process produces bolts whose mean length is 125
millimeters with a standard deviation of 1 millimeter with a bellshaped distribution of lengths. Can you be sure that more than 95%
of the bolts are acceptable? Explain.