The goal of corporate sustainability is to manage the environmental, economic, and social effects of a corporation’s operations so it is profitable over the long term while acting in a responsible manner toward society. A Hill $Knowlton Strategies survey found that 57% of U. S. respondents are more likely to buy stock in a U. S. corporation, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable. Suppose you select a sample of 100 U. S. respondents.

a. What is the probability that in the sample, fewer than 57% are more likely to buy stock in a U. S. corporation, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?

b. What is the probability that in the sample, between 52% and 62% are more likely to buy stock in a U. S. corporation, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?

c. What is the probability that in the sample, more than 62% are more likely to buy stock in a U. S. corporation, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?

d. If a sample of 400 is taken, how does this change your answers to (a) through (c)?