The diameter of a ball is a random variable X with the next density:

2x if 0<x<=0.5

1 if 0.5<x<=1

f(X)= 0.25 if 1<x<=2

0 else

a. What is the diameter of balls that half of the diamteres will be smaller than him (median) ?

b. What is the probability that among 50 balls (chosen randomly), at least 30 balls will have a diameter of more than 0.5 ?