Question

The lengths of one-year-old baby girls can be described using a normal distribution with a mean of 29 inches and a standard deviation of 1.2 inches. using the empirical '68-95-99.7' rule, what percent of one-year-old girls are shorter than 31.4 inches?

Answer 1

The '68-95-99.7' rule says

-About 68% of values fall within one standard deviation of the mean.

-About 95% of the values fall within two standard deviations from the mean.

-Almost all of the values — about 99.7% — fall within three standard deviations from the mean.

Here $31.4=29+2*1.2 26.6=29-2*1.2$

Therefore, the probability

$P(26.6<L<31.4)=0.95$

The required probability

$P(L<31.4)=0.95+\frac{1-0.95}{2} =0.975$