5.45 It is known that 10% of all the items produced by a particular manufacturing process are defective. From the very large output of a single day, 400 items are selected at random.

a. What is the probability that at least 35 of the selected items are defective?

b. What is the probability that between 40 and 50 of the selected items are defective?

c. What is the probability that between 34 and 48 of the selected items are defective?

d. Without doing the calculations, state which of the following ranges of defectives has the highest probability:
38–39, 40–41, 42–43, 44–45, or 46–47.