Chapter 11.1, Problem 27PPS

a.

To determine

To simulate the experiment for product A and use the random number generator on a graphing calculator.

Explanation of Solution

Given:

The product A is $70\%$ effective and product B is $80\%$ effective.

Calculation:

Let us first simulate the experiment for product A. Use the random number generator on a graphing calculator to generate 30 integers between 0 and 9. Let 0-6 represent an effective outcome and 7-9 represent an ineffective outcome. Use TI-83 Calculator for random number generator. The procedure is given as below;

1. Switch ON the calculator and bring up the CATALOG by pressing 2nd followed by the digit 0. Select the randInt( function as shown below by pressing ENTER.

  

2. Complete the function by as shown below to generate a random number between 0 and 9.

  

Repeat 30 times to get 30 integers between 0 and 9. A sample list of generated integers is given as 0, 9, 0, 4, 6, 2, 2, 3, 1, 3, 5, 0, 8, 0, 7, 8, 6, 2, 1, 1, 6, 0, 9, 2, 0, 7, 3, 1, 8, and 7. Thus, there are 22 effective outcomes and 8 ineffective outcomes.

Repeat the process to simulate an experiment for Product B. Use the random number generator on a graphing calculator ..., let 0-7 represent an effective outcome and 8-9 represent an ineffective outcome. A sample list of generated integers is 5, 9, 0, 0, 7, 8, 0, 1, 9, 2, 4, 3, 3, 5, 9, 1, 4, 4, 1, 5, 7, 0, 5, 9, 6, 2, 7, 3, 2, and 4. Thus, there are 25 effective outcomes and 5 ineffective outcomes.

b.

To determine

To find the probability of product A being effective and product B being effective.

Answer to Problem 27PPS

  $70.33\%,80.33\%$

Explanation of Solution

Given:

The product A is $70\%$ effective and product B is $80\%$ effective.

Calculation:

The frequency tables for Product A and Product B are shown below.

Product A:

Number	Frequency
0-6	22
7-9	8

Product B

Number	Frequency
0-6	25
7-9	5

The probability that Product A was effective is:

  $=\frac{22}{30}=70.33\%$

Similarly, the probability that Product B was effective is:

  $=\frac{25}{30}=80.33\%$

c.

To determine

To compare the probabilities and to tell the difference in the effectiveness of one product over the other.

Explanation of Solution

Given:

The product A is $70\%$ effective and product B is $80\%$ effective.

Calculation:

Based on the obtained probabilities in the part (b), it is justifiable to select Product B over Product A as it has a higher number of effective outcomes and the difference of 10% in the probabilities is a significant one.

d.

To determine

To explain that the probability of the product’s effectiveness justifies the price difference.

Explanation of Solution

Given:

The product A is $70\%$ effective and product B is $80\%$ effective.

Calculation:

It depends on the actual product. For generic products, the 10% higher effectiveness of Product B might not be justifiable for twice the cost. But if Product B is a life-saving drug, the price difference might be justified because effectiveness of the medicine is more important than the price.