Answered: The accounting department at Weston…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The accounting department at Weston Materials Incorporated, a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution

.a-1. Determine the z-values for 29 and 34 hours. (A negative amount should be indicated by a minus sign. Round z-value to 2 decimal places and your final answer to 2 decimal places.)

a-2. What percent of the garages take between 32 hours and 34 hours to erect? (Round z-value to 2 decimal places and your final answer to 2 decimal places.)

b. What percent of the garages take between 29 hours and 34 hours to erect? (Round z-value to 2 decimal places and your final answer to 2 decimal places.)

c. What percent of the garages take 28.7 hours or less to erect? (Round z-value to 2 decimal places and your final answer to 2 decimal places.)

d. Of the garages, 5% take how many hours or more to erect? (Round your answer to 1 decimal place.)

**Title:** Understanding Time Distribution for Garage Erection

The accounting department at Weston Materials Incorporated, a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.

### a-1. Z-Value Calculation
Determine the z-values for 29 and 34 hours.
(Note: A negative amount should be indicated by a minus sign. Round z-value to 2 decimal places and your final answer to 2 decimal places.)

- **29 hours corresponds to z:** [Input Field]
- **34 hours corresponds to z:** [Input Field]

### a-2. Percentage for 32 to 34 Hours
Calculate the percentage of garages that take between 32 hours and 34 hours to erect.
(Round z-value to 2 decimal places and your final answer to 2 decimal places.)

- **Percentage:** 77.45%

### b. Percentage for 29 to 34 Hours
Calculate the percentage of garages that take between 29 hours and 34 hours to erect.
(Round z-value to 2 decimal places and your final answer to 2 decimal places.)

- **Percentage:** [Input Field] %

### c. Percentage for 28.7 Hours or Less
Calculate the percentage of garages that take 28.7 hours or less to erect.
(Round z-value to 2 decimal places and your final answer to 2 decimal places.)

- **Percentage:** 4.95%

### d. Identification of Outliers
Determine how many hours or more 5% of the garages take to erect.
(Round your answer to 1 decimal place.)

- **Hours:** [Input Field]

This exercise illustrates the application of the normal distribution to real-world scenarios by examining how data such as time for construction can be analyzed to determine percentages and identify operational efficiencies.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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