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 five people who are given a sales talk about a new, improved product.
(a) Make a histogram showing the probability that r = 0 to 5 people believe the product is, in fact, improved.
(b) Compute the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.) μ = people σ = people
(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? (Hint: Note that P(r ≥ 1) = 0.99 is equivalent to 1 - P(0) = 0.99, or P(0) = 0.01.) people