A Meteorologist Predicts That the Amount of Rainfall (In Inches) $f ( x ) = \frac { \pi } { 30 } \sin \frac { \pi x } { 15 },$

Multiple Choice

A meteorologist predicts that the amount of rainfall (in inches) expected for a certain coastal community during a hurricane has the probability density function $f ( x ) = \frac { \pi } { 30 } \sin \frac { \pi x } { 15 },$ $0 \leq x \leq 15$ . Find and interpret the probability $P ( 0 \leq x \leq 5 )$ .

A) 17% probability of receiving up to 5 inches of rain
B) 25% probability of receiving up to 5 inches of rain
C) 30% probability of receiving up to 5 inches of rain
D) 75% probability of receiving up to 5 inches of rain
E) 83% probability of receiving up to 5 inches of rain