Question

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

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

Answer 1

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