The Time T (In Hours) Required for a New Employee $f ( t ) = \frac { 5 } { 324 } t \sqrt { 9 - t }$

Multiple Choice

The time t (in hours) required for a new employee to successfully learn to operate a machine in a manufacturing process is described by the probability density function $f ( t ) = \frac { 5 } { 324 } t \sqrt { 9 - t }$ over the interval $[ 0,9 ]$ . Find the probability that a new employee will learn to operate the machine in more than 3 hours but less than 7 hours.

A) 0.6634
B) 0.3052
C) 0.5895
D) 0.2733
E) 0.4632