Question

About what percent of the cockroaches have weights between $76$ and $84$ grams?

(a) $99.7\%$

(b) $95\%$

(c) $68\%$

(d) $47.5\%$

(e) $34\%$

Short answer

The correct answer is (b)$95\%$.

Step-by-step solution

Given Information

$68-95-99.7$ rule

Approximately $68\%$ of the observations are within $1$ standard deviation of the mean.

Approximately $95\%$ of the observations are within $2$ standard deviations of the mean.

Approximately $99.7\%$ of the observations are within $3$ standard deviations of the mean.

Explanation

Mean $=80$

Standard deviation $=2$

There is a $2$standard deviation difference between $76$and the mean.

$(\mu -2\sigma =80-2(2)=80-4=76)$

There is a $2$standard deviation difference between $84$and the mean.

$(\mu +2\sigma =80+2(2)=80+4=84)$

As a result of the $68-95-99.7$ rule, approximately $95\%$ of the data values fall within $2$ standard deviations of the mean and thus approximately $95\%$ of the cockroaches will be between $76$ and $84$ grams in weight.