3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 x² (4 − x) 0 64 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
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3. The level of impurity (in percent) in the product of a certain chemical process is a random variable
with probability density function
3
64
-x²(4 - x)
0
0 < x < 4
otherwise
a. What is the probability that the impurity level is greater than 3%?
b. What is the probability that the impurity level is between 2% and 3%?
c. Find the mean impurity level.
d. Find the variance of the impurity levels.
Transcribed Image Text:3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.
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