Chapter 2.2, Problem 87E

To determine

To find: The proportion of cockroaches that weight between 76 and 84 grams.

Answer to Problem 87E

The required proportion is 95%

Explanation of Solution

Given:

Population mean (µ) = 80

Population standard deviation (s) = 2

Calculation:

Consider, X be the random variable that shows the weight of cockroaches in grams.

The proportion of cockroaches that weight between 76 and 84 grams can be calculated as:

  $\begin{array}{c}P\left(76<X<84\right)=P\left(\frac{76-\mu }{\sigma }<Z<\frac{84-\mu }{\sigma }\right)\\ =P\left(\frac{76-80}{2}<Z<\frac{84-80}{2}\right)\\ =P\left(-2<Z<2\right)\\ =0.95\end{array}$

Thus, the required proportion is approximately 95%

Hence, the correct option is (b).