The authors generac generator produces voltage amounts with a mean of 125.6 volts and a standard deviation of 0.3 volt. using the Chebyshev's theorem, what do we know about the percentage of voltage amounts that are within 3 standard deviations of the mean? what are the minimum and maximum voltage amounts that are within 3 standard deviation of the mean?

Answer 1

This theorem says:

1. Within two standard deviations of the mean, you will find at least 75% of the data.
2. Within three standard deviations of the mean, you will find at least 89% of the data.

Here's how the formula shows this:

Formula is 1 - (1/k^2) ---> ^2 means squared.

If k = 2 (representing two standard deviations), we have this:
1 - (1/2^2) = 1 - (1/4) = 3/4 or .75 or 75%

If k = 3 (representing three standard deviations), we have this:
1 - (1/3^2) = 1 - (1/9) = 8/9 or approximately .89 or 89%

I'll let you take it from here.