The length of time (in days) required to complete a certain task is a random variable t with probability density function defined by f(t) = e- for t in [0, ∞0) 2 (a) Determine the mean of the distribution. f(t) (b) Determine the standard deviation of the distribution. (c) Find the probability (not percentage) that the time required to complete a certain task is no more than 6 days. Round your answer to four decimal places as needed. (d) Find the probability (not percentage) that the time required to complete a certain task is between the mean and one standard deviation above the mean. Round your answer to four decimal places as needed.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 20E
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The length of time (in days) required to complete a certain task is a random variable t with probability
density function defined by
f(t)
=
e-
for t in [0, ∞0)
2
(a) Determine the mean of the distribution.
f(t)
(b) Determine the standard deviation of the distribution.
(c) Find the probability (not percentage) that the time required to complete a certain task is no more than
6 days. Round your answer to four decimal places as needed.
(d) Find the probability (not percentage) that the time required to complete a certain task is between the
mean and one standard deviation above the mean. Round your answer to four decimal places as needed.
Transcribed Image Text:The length of time (in days) required to complete a certain task is a random variable t with probability density function defined by f(t) = e- for t in [0, ∞0) 2 (a) Determine the mean of the distribution. f(t) (b) Determine the standard deviation of the distribution. (c) Find the probability (not percentage) that the time required to complete a certain task is no more than 6 days. Round your answer to four decimal places as needed. (d) Find the probability (not percentage) that the time required to complete a certain task is between the mean and one standard deviation above the mean. Round your answer to four decimal places as needed.
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