9. If acceptable air quality in Omak during the summer is normally distributed with a mean of 80 and a standard deviation of 9, and the following data were collected over the last 14 days: Day 1 2 3. 74 5 11 12 13 14 4. 9. 8. Air 75 08 quality 98 65 75 75 85 601 901 08 08 a. Sketch a control chart to determine if the air quality during these 14 days was acceptable. b. Is the air quality out of control? And if so what type of signal?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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9.
If acceptable air quality in Omak during the summer is normally distributed with a mean of 80 and a standard
deviation of 9, and the following data were collected over the last 14 days:
7.
60T
97
Day
2
11
12
13
14
4.
8.
1.
6.
9.
Air
75
74
87
65
75
75
85
98
901
08
08
quality
a. Sketch a control chart to determine if the air quality during these 14 days was acceptable.
b. Is the air quality out of control? And if so what type of signal?
Ans.
II
Transcribed Image Text:9. If acceptable air quality in Omak during the summer is normally distributed with a mean of 80 and a standard deviation of 9, and the following data were collected over the last 14 days: 7. 60T 97 Day 2 11 12 13 14 4. 8. 1. 6. 9. Air 75 74 87 65 75 75 85 98 901 08 08 quality a. Sketch a control chart to determine if the air quality during these 14 days was acceptable. b. Is the air quality out of control? And if so what type of signal? Ans. II
Expert Solution
Step 1

The control charts are used in the statistical quality control as a powerful tool for discovering and correcting the assignable causes of variations outside the stable pattern of chance causes. It therefore, helps to stabilize and control the processes at desired performances and bring the process under statistical control.

Where, the assignable causes are due to human error and  can be resolved, while the chance causes are  beyond human control and thus can not be eliminated.

The control charts are of eight types in total which are divided for process control and product control and further  for variable and attribute.

The control chart used to control the mean and standard deviation of the process are X¯ charts for average and range respectively.

The first step to construct a control chart after selecting the sample is to set the control limits.

The standards are known, so the formula to set the control limit for X-Chart is:

E(X)±3.S.E(X)=μ±3.σn

 

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