MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.
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Transcribed Image Text:**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.
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Step 1: Define the formula of Z-score
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Step 2: Obtain the Z-score values for X equals 29 and 34 hours.
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Step 3: Obtain the percent of the garages take between 32 hours and 34 hours to erect.
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Step 4: Obtain the percent of the garages take between 29 hours and 34 hours to erect.
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Step 5: Obtain the percent of the garages take 28.7 hours or less to erect.
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Step 6: Determine the number of hours that takes to erect.
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Solution
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