 # Suppose the amount of liquid dispensed by a certain machine is uniformly distributed with lower limit A = 8 oz and upper limit B = 10 oz. Describe how you would carry out simulation experiments to compare the sampling distribution of the (sample) fourth spread for sample sizes n = 5, 10, 20, and 30. ### Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809 ### Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

#### Solutions

Chapter
Section
Chapter 5.3, Problem 43E
Textbook Problem

## Suppose the amount of liquid dispensed by a certain machine is uniformly distributed with lower limit A = 8 oz and upper limit B = 10 oz. Describe how you would carry out simulation experiments to compare the sampling distribution of the (sample) fourth spread for sample sizes n = 5, 10, 20, and 30.

Expert Solution
To determine

Describe the procedure to carry out the simulation experiments in order to compare the sampling distribution of the sample fourth spread for sample sizes n=5, 10, 20 and 30.

### Explanation of Solution

Given info:

The amount of liquid dispensed by a machine has a uniform distribution with lower limit A=8 oz and upper limit B=10 oz.

Calculation:

The fourth spread is a measure of spread in a data, which is resistant to the presence of outliers and is given by fs=upper fourthlower fourth, where the lower fourth and the upper fourth are respectively the median of the smallest half and the median of the largest half.

Let X be the amount of liquid (oz) dispensed by a machine. Here, X has a uniform distribution with lower limit A=8 oz and upper limit B=10 oz. The probability density function (pdf) of a uniform random variable is:

f(x;A,B)={1BA,  AXB0,          otherwise.

Thus, the pdf of X is:

f(x;8,10)=1108=12=0

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