Chapter 12.7, Problem 8PPS

a.

To determine

To write a simulation for finding the possible outcome for the pairs of jeans having defects.

Answer to Problem 8PPS

On possible simulation is, $\text{16}$ marbles in a bag, and $\text{1}$ marble is drawn at random. The marbles represent the jeans.

Explanation of Solution

Given information:

The given statement is:

“Julie examines the stitching on pairs of jeans that are produced at a manufacturing plant. She expects to find defects in $\text{1}$ out of every $\text{16}$ pairs.”

On possible simulation is, $\text{16}$ marbles in a bag, and $\text{1}$ marble is drawn at random. The marbles represent the jeans.

b.

To determine

To find the expected value that a random pair of jeans has a defect.

Answer to Problem 8PPS

The expected value that a random pair of jeans has a defect is $\frac{1}{16}\text{ or 6}\text{.25\%}$ .

Explanation of Solution

Given information:

The given statement is:

“Julie examines the stitching on pairs of jeans that are produced at a manufacturing plant. She expects to find defects in $\text{1}$ out of every $\text{16}$ pairs.”

The expected value that a random pair of jeans has a defect is $\frac{1}{16}\text{ or 6}\text{.25\%}$ .

c.

To determine

To find the experimental probability that a random pair of jeans will have a defect.

Answer to Problem 8PPS

Experimental probability of getting a defect is $\frac{61}{1600}\text{ or 3}\text{.8\%}$ .

Explanation of Solution

Given information:

The results of simulations using Julie’s expectations are shown:

  

Calculation:

The total defect is shown in the table:

  

After $100$ simulations, or $1600$ drawings, $61$ has defect.

Experimental probability of getting a defect is $\frac{61}{1600}\text{ or 3}\text{.8\%}$ .

d.

To determine

To compare the experimental probability and the expected value.

Answer to Problem 8PPS

There is a significant difference between the expected value and the experimental probability for finding the defect in the pair of jeans.

Explanation of Solution

Given information:

The expected value is $\frac{1}{16}\text{ or 6}\text{.25\%}$ and the experimental probability is $\frac{61}{1600}\text{ or 3}\text{.8\%}$ .

There is a significant difference between the expected value and the experimental probability for finding the defect in the pair of jeans.