Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Textbook Question
Chapter 1.5, Problem 1.17E
Refer to Exercise 1.16. Construct a relative frequency histogram for the data.
a. Approximately how many class intervals should you use?
b. Suppose you decide to use classes starting at 1.6 with a class width of.5 (i.e., 1.6 to <2.1,2.1 to <2.6). Construct the relative frequency histogram for the data.
c. What fraction of the measurements are less than 5.1?
d. What fraction of the measurements are larger than 3.6?
e. Compare the relative frequency histogram with the stem and leaf plot in Exercise 1.1 6. Are the shapes similar?
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A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected.
a) Calculate the percentage of components that get rejected.
b) In a manufacturing run of 1000 units, how many are expected to be rejected?
c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.
5. Let X and Y be independent random variables and let the superscripts denote
symmetrization (recall Sect. 3.6). Show that
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8. Suppose that the moments of the random variable X are constant, that is, suppose
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Chapter 1 Solutions
Introduction to Probability and Statistics
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