The Daily Demand $x$ For a Certain Product (In Hundreds of Pounds) Is a of Pounds)

Multiple Choice

The daily demand $x$ for a certain product (in hundreds of pounds) is a random variable with the probability density function $f ( x ) = \frac { 2 } { 9 } x ( 3 - x )$ over the interval $[ 0,3 ]$ . Find the probability that $x$ is within one standard deviation of the mean. Express your answer as a percent.

A) 96.44 $\%$
B) 49.28 $\%$
C) 62.61 $\%$
D) 13.41 $\%$
E) 72.77 $\%$