The Empirical Rule affirm:
99.7 % random variable values are between
±
three standard deviation.
95 % random variable values are between
±
two standard deviation.
68 % random variable values are between
±
one standard deviation. There you go!
Jane: Think: the hypotenuse of her ramp is 14 inches and the angle opposite the rise is 30 degrees. Thus, cos 30 deg = (adj side) / (hyp) = (adj side) / (14 in).
Solving for (adj side), we get (adj side) = (14 in)(sqrt(3)/2) = 7 sqrt(3) inches.