"The graph of a normal curve is given. Use the graph to identify the values of #\mu# and #\sigma#" ?

computer

Answer: #\mu=100,\sigma=15#
Issue: Why? Looks like #\sigma=3# to me...

1 Answer
SCooke
Jul 22, 2017

EACH division indicated is ONE #sigma# = 15 units. The "#3sigma# point" is at 145. "+/-#3sigma#" is the interval from 55 to 145.

Explanation:

Don't confuse the metric with the range used for a desired accuracy. The +/- #3-sigma# range is used for 99.7% probability of a true value, but the initial #sigma" value is calculated from the data variation.

In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively. (Ref.: https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule )

See also: http://www.emu.edu.tr/~oyagiz/MGMT585/Six%20Sigma%20vs_%20Three%20Sigma.htm

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