anonymous
  • anonymous
STATISTICS: In a study of 500 men, diastolic blood pressure was found to be approx. normally distributed, with a mean of 82mm of mercury and a standard deviation of 10mm. Question: Use the 68-95-99.7% rule to determine what percentage of the test group had a diastolic pressure between 72mm and 92mm of mercury.
Mathematics
jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
draw the normal bell curve |dw:1444168819721:dw|
jim_thompson5910
  • jim_thompson5910
at the center is the mean 82 |dw:1444168888474:dw|
jim_thompson5910
  • jim_thompson5910
plot 72 and 92 on there as well |dw:1444168948036:dw|

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jim_thompson5910
  • jim_thompson5910
with me so far?
anonymous
  • anonymous
yes!
jim_thompson5910
  • jim_thompson5910
how far is 72 from 82?
anonymous
  • anonymous
10
jim_thompson5910
  • jim_thompson5910
yes, and because we have a `standard deviation of 10mm`, this means that 72 is ONE full standard deviation away from the mean |dw:1444169140982:dw|
jim_thompson5910
  • jim_thompson5910
92 is also ten units away from the mean of 82 92 is 1 standard deviation away from the mean |dw:1444169186031:dw|
jim_thompson5910
  • jim_thompson5910
the `68-95-99.7% rule`says that roughly 68% of the entire distribution is within 1 standard deviation. This shaded region has an area of roughly 0.68 |dw:1444169247011:dw|
jim_thompson5910
  • jim_thompson5910
`68-95-99.7% rule` or `empirical rule` http://www.oswego.edu/~srp/stats/6895997.htm
anonymous
  • anonymous
Ahh, thank you so much! @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
no problem

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