Statistical Techniques in Business and Economics
18th Edition
ISBN: 9781260579611
Author: Douglas Lind; William Marchal; Samuel Wathen
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 7, Problem 1SR
Microwave ovens only last so long. The life-time of a microwave oven follows a uniform distribution between 8 and 14 years.
- (a) Draw this uniform distribution. What are the height and base values?
- (b) Show the total area under the curve is 1.00.
- (c) Calculate the mean and the standard deviation of this distribution.
- (d) What is the
probability a particular microwave oven lasts between 10 and 14 years? - (e) What is the probability a microwave oven will last less than 9 years?
a.
Expert Solution
To determine
Draw the uniform distribution graphically.
Find the height and base values of distribution.
Answer to Problem 1SR
The height and base values of the distribution are 0.167 and 6, respectively.
Explanation of Solution
Step-by-step procedure to obtain the uniform distribution using MINITAB software:
- Choose Graph > Probability Distribution Plot.
- From Distribution, choose Uniform.
- Enter Lower endpoint as 8 and Upper endpoint as 14.
- Click Ok.
The output obtained using MINITAB software is represented as follows:
From the above output, the shape of the distribution is rectangle.
The height of the distribution is calculated below:
Therefore, the height of the distribution is 0.167.
The base of the distribution is obtained below:
The base value of the distribution is 6.
b.
Expert Solution
To determine
Prove that the total area under the curve is 1.00
Explanation of Solution
Let X is the life-time of a microwave oven which follows uniform distribution over the interval from 8 and 14 years.
That is,
The probability density function of a uniform distribution is,
The height and base values of the distribution are 0.167 and 6 respectively.
The area under the curve is obtained below:
Therefore, the total area under the curve is 1.
c.
Expert Solution
To determine
Compute the mean and standard deviation of the distribution.
Answer to Problem 1SR
The mean of the distribution is 11.
The standard deviation of the distribution is 1.73.
Explanation of Solution
The formula for mean of the distribution is stated below:
The mean life-time of a microwave oven is 11.
The formula for standard deviation of the distribution is computed below:
Therefore, the standard deviation of the distribution is 1.73.
d.
Expert Solution
To determine
Find the probability that a particular microwave oven lasts between 10 and 14 years.
Answer to Problem 1SR
The probability that a particular microwave oven lasts between 10 and 14 years is 0.668.
Explanation of Solution
The height of the distribution is 0.167 and base of the distribution is 4 ( = 14 – 10).
The probability that a particular microwave oven lasts between 10 and 14 years is,
Therefore, the probability that a particular microwave oven lasts between 10 and 14 years is 0.668.
e.
Expert Solution
To determine
Find the probability that a microwave oven will last less than 9 years.
Answer to Problem 1SR
The probability that a particular microwave oven will last less than 9 years is 0.167.
Explanation of Solution
The height of the distribution is 0.167 and base of the distribution is 1.
The probability that a particular microwave oven will last less than 9 years is calculated below:
Therefore, the probability that a particular microwave oven will last less than 9 years is 0.167.
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Students have asked these similar questions
Microsoft Excel include formulas
Question 1
The data shown in Table 1 are and R values for 24 samples of size n = 5 taken from a process producing
bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals
recorded (i.e., 34.5 should be 0.50345).
Table 1: Bearing Diameter Data
Sample Number
I
R
Sample Number
I R
1
34.5
3
13
35.4
8
2
34.2
4
14
34.0
6
3
31.6
4
15
37.1
5
4
31.5
4
16
34.9
7
5
35.0
5
17
33.5
4
6
34.1
6
18
31.7
3
7
32.6
4
19
34.0
8
8
33.8
3
20
35.1
9
34.8
7
21
33.7
2
10
33.6
8
22
32.8
1
11
31.9
3
23
33.5
3
12
38.6 9
24
34.2
2
(a) Set up and R charts on this process. Does the process seem to be in statistical control? If necessary,
revise the trial control limits. [15 pts]
(b) If specifications on this diameter are 0.5030±0.0010, find the percentage of nonconforming bearings pro-
duced by this process. Assume that diameter is normally distributed. [10 pts]
1
4. (5 pts) Conduct a chi-square contingency test (test of independence) to assess whether
there is an association between the behavior of the elderly person (did not stop to talk,
did stop to talk) and their likelihood of falling. Below, please state your null and
alternative hypotheses, calculate your expected values and write them in the table,
compute the test statistic, test the null by comparing your test statistic to the critical
value in Table A (p. 713-714) of your textbook and/or estimating the P-value, and
provide your conclusions in written form. Make sure to show your work.
Did not stop walking to talk
Stopped walking to talk
Suffered a fall
12
11
Totals
23
Did not suffer a fall | 2
Totals
35
37
14
46
60
T
Chapter 7 Solutions
Statistical Techniques in Business and Economics
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