The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a continuous random variable X that has the density function shown below. Find the probability that over a period of one year, a family runs their vacuum cleaner (a) less than 105 hours; (b) between 65 and 100 hours. X, 0

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter11: Simulation Models
Section11.5: Simulating Games Of Chance
Problem 37P: The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three...
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The total number of hours, measured
in units of 100 hours, that a family runs
a vacuum cleaner over a period of one
year is a continuous random variable X
that has the density function shown
below. Find the probability that over a
period of one year, a family runs their
vacuum cleaner (a) less than 105
hours; (b) between 65 and 100 hours.
X,
0<x<1
f(x) =
2-x, 1<x<2
0,
elsewhere
Question content area bottom
Part 1
(a) The probability the family runs the
vacuum cleaner less than 105 hours is
enter your response here.
(Type an integer or decimal rounded to
three decimal places as needed.)
Transcribed Image Text:The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a continuous random variable X that has the density function shown below. Find the probability that over a period of one year, a family runs their vacuum cleaner (a) less than 105 hours; (b) between 65 and 100 hours. X, 0<x<1 f(x) = 2-x, 1<x<2 0, elsewhere Question content area bottom Part 1 (a) The probability the family runs the vacuum cleaner less than 105 hours is enter your response here. (Type an integer or decimal rounded to three decimal places as needed.)
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