Chapter 2.2, Problem 88E

To determine

To find: The proportion of cockroaches that weigh more than 83 grams.

Answer to Problem 88E

The required proportion is 0.0668.

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 weigh more than 83 grams can be calculated as:

  $\begin{array}{c}P\left(X>83\right)=P\left(\frac{x-\mu }{\sigma }>\frac{83-\mu }{\sigma }\right)\\ =P\left(Z>\frac{83-80}{2}\right)\\ =P\left(Z>1.5\right)\\ =0.0668\end{array}$

Thus, the required proportion is approximately 0.0668.

Hence, the correct option is (b).