The amount of bread ,X (in 100 pounds) that a certain bakery is able to sell in a day is found to be

a numerically valued random phenomenon with a probability density function specified by f(x) given below;

,0 5

( ) (10 ),5 10

0,

Ax x

f x A x x

otherwise

a) Find the value of A such that

f x

is a pdf.

b) What is the probability that the number of pounds of bread that will be sold tomorrow will be more than 500 pounds,less then 500 pounds and between 250 and 750 pounds