(a) Fiberglass manufacturing company finds 10% defective items in their production output. The production manager has been instructed to analyze and recommend solutions for improving the process. If a sample of 20 items is inspected, what is the probability of finding exactly two or three defectives?

(b) An emergency unit at the local hospital has admitted an average of 20 patients per hour. What is the probability that the next patient will be admitted at least 5 minutes from now?

(c) It is observed that the average share prices of ANZ Bank are normally distributed with a mean of $27 and a standard deviation of $2.

(i) What proportion of the share prices is between $25 and $35?

(ii) What value do the upper 5% of the share prices exceed?