The level of impurity (in percent) in the product of a certain chemical process is a random

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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 <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.

e. Find the cumulative distribution function of the impurity level.

Distribution
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