Baby worms grow from a length of 0.5 mm to a length of 1.0 mm. After a day of growth, the measurement L representing length has p.d.f.
f (l) = 1.5(1 +l2)
for 0.5 ≤ l ≤ 1.0.
a. Graph the p.d.f. and check that it is consistent.
b. Find the probability that a worm is less than 0.75 mm long.
c. Find the approximate probability that a worm is between 0.75 and 0.76 mm long.
d. How many worms out of 1000 would you expect to be longer than 0.75 mm?