#probability solutions

[engineeringmath]

Mean and Variance | Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.10

For the data of Exercise 1.4 on page 13, compute both the mean and variance in "flexibility" for both company A and company B. 

For the data of Exercise 1.4 on page 13, compute both the mean and variance in “flexibility” for both company A and company B.  Solution:

For the company A:

We know, based on our answer in Exercise 1.4, that the sample mean for samples in Company A is .

To compute for the sample variance, we shall use the formula

The formula states that we need to get the sum of , so we can use a table…

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[engineeringmath]

Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.9

Exercise 1.3 on page 13 showed samples of tensile strength data, one for specimens that were exposed to an aging process and one in which there was no aging of the specimens. Calculate the sample variance as well as standard deviation in tensile strength for both samples. 

Solution:

For the samples with NO AGING:

We know, based on our answer in Exercise 1.3, that the sample mean for…

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[engineeringmath]

Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.8

Compute the sample variance and standard deviation for the water absorbency data of Exercise 1.2 on page 13.

Solution:

We know, based on our answer in Exercise 1.2, that the sample mean is .

To compute for the sample variance, we shall use the formula

The formula states that we need to get the sum of , so we can use a table to solve for every sample.

Note: You can refer to the solu…

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[engineeringmath]

Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.3

A certain polymer is used for evacuation systems for aircraft. It is important that the polymer be re­sistant to the aging process. Twenty specimens of the polymer were used in an experiment. Ten were assigned randomly to be exposed to the accelerated batch aging process that involved exposure to high tempera­tures for 10 days. Measurements of the tensile strength of the specimens were made and the following data were recorded on tensile strength in psi. No aging: 227 222 218 217 225 218 216 229 228 221 Aging: 219 214 215 211 209 218 203 204 201 205 (a) Do a dot plot of the data. (b) From your plot, does it appear as if the aging pro­cess has had an effect on the tensile strength of this polymer? Explain. (c) Calculate the sample mean tensile strength of the two samples. (d) Calculate the median for both. Discuss the simi­larity or lack of similarity between the mean and median of each group. Click the link for solution

A certain polymer is used for evacuation systems for aircraft. It is important that the polymer be re­sistant to the aging process. Twenty specimens of the polymer were used in an experiment. Ten were assigned randomly to be exposed to the accelerated batch aging process that involved exposure to high tempera­tures for 10 days. Measurements of the tensile strength of the specimens were made and…

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[engineeringmath]

Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.1

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.0 5.2 3.0 4.8 Assume that the measurements are a simple random sample. a) What is the sample size for the above sample? b) Calculate the sample mean for this data. c) Calculate the sample median. d) Plot the data by way of a dot plot. e) Compute the 20% trimmed mean for the above data set.

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The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint

3.42.54.82.93.62.83.35.63.72.84.44.05.23.04.8

Assume that the measurements are a simple random sample.

a) What is the sample size for the above sample?

b) Calculate the sample mean for this data.

c) Calculate the sample median.

d) Plot the data by way of a dot plot.

e) Compute…

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