Question: A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 20% of all its current stockholders. Suppose that this belief is correct. A random sample of 130 current stockholders is taken.

(a) What is the probability that the proportion of stockholders in this sample interested in the offer is more than 15%?

(b) What is the probability that the proportion of stockholders in this sample interested in the offer is between 18% and 22%?

(c) Suppose that a sample of 500 stockholders had been taken. Without doing the calculations state if the probabilities obtained in (a) and (b) would be higher, lower or the same as those found.