If a distribution is mound-shaped and symmetric, what percent of homes will have a monthly bill of more than $115? The mean monthly bill is $125 and has a standard deviation of $10.

Answer 1

Well, $115 is exactly one SD below the mean, so that's handy.

A useful guideline is that, moving left to right, over 2SD covers the first 2%; 2-to-1 SD is another 14%, bringing you up to 16%, and 1-to-0 SD covers another 33%, bringing you to the mean at 50% (not quite, because I've omitted the decimals, but the 1/3 and 1/6 rules are easy to remember.)

So about 16% will be below 1SD below the mean, which is about 16% of homes having a monthly bill of _less_ that $115.

If you want more accuracy, Google yourself a z-score table and read off the exact percentile.