The Wall Street Journal reported that approximately 25% of the people who are told a product is improved will believe that it is, in fact, improved. The remaining 75% believe that this is just hype (the same old thing with no real improvement). Suppose a marketing study consists of a random sample of eight people who are given a sales talk about a new, improved product.

(a) Make a histogram showing the probability that r 5 0 to 8 people believe the product is, in fact, improved.

(b) Compute the mean and standard deviation of this probability distribution.

(c) How many people are needed in the marketing study to be 99% sure that at least one person believes the product to be improved?

Note that P(r ( 1) = 0.99 is equivalent to 1 - P(0) - 0.99, or P(0) - 0.01.