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A continuous variable x is said to have a uniform distri- bution if the density function is given by f(x): b a

A continuous variable x is said to have a uniform distri- bution if the density function is given by f(x): b a

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A continuous variable x is said to have a uniform distri- bution if the density function is given by -{+-+ b = 0 f(x) a<x<b otherwise The corresponding density "curve" has constant height over the interval from a to b. Suppose the time (min) taken by a clerk to process a certain application form has a uniform distribution with a = 4 and b = 6. a. Draw the density curve, and verify that the total area under the curve is indeed 1. b. In the long run, what proportion of forms will take between 4.5 min and 5.5 min to process? At least 4.5 min to process? c. What value separates the slowest 50% of all pro- cessing times from the fastest 50% (the median of the distribution)? d. What value separates the best 10% of all process- ing times from the remaining 90%?
Transcribed Image Text:A continuous variable x is said to have a uniform distri- bution if the density function is given by -{+-+ b = 0 f(x) a<x<b otherwise The corresponding density "curve" has constant height over the interval from a to b. Suppose the time (min) taken by a clerk to process a certain application form has a uniform distribution with a = 4 and b = 6. a. Draw the density curve, and verify that the total area under the curve is indeed 1. b. In the long run, what proportion of forms will take between 4.5 min and 5.5 min to process? At least 4.5 min to process? c. What value separates the slowest 50% of all pro- cessing times from the fastest 50% (the median of the distribution)? d. What value separates the best 10% of all process- ing times from the remaining 90%?
Expert Solution
Step 1: Determine the given variable

Given that continuous variable

               X tilde U open parentheses a comma b close parentheses

if the density function is

               f left parenthesis x right parenthesis equals open curly brackets table row cell fraction numerator 1 over denominator b minus a end fraction space space space space space space space space space a less than x less than b end cell row cell space space space space 0 space space space space space space space space space space space space o t h e r w i s e end cell end table close

The time taken by the clerk to process a certain application form has a uniform distribution with a=4 and b=6.

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