Question: For a normal curve approximation of the binomial distribution to be acceptable, all possible values of x should be between 0 and n, which are the lower and upper limits, respectively, of a binomial distribution. If µ±3σ is not between 0 and n, do not use the normal approximation of the binomial distribution.

Suppose the International Data Corporation reports that Compaq is number one in PC market share in the United States with 16% of the market. Suppose a researcher randomly selects 130 recent purchasers of PC’s.

a. Show that the normal approximation to the binomial distribution is appropriate here.

b. What is the probability that more than 25 PC purchases bought a Compaq?

c. What is the probability that between 15 and 23 (inclusive) PC purchasers bought a Compaq?

d. What is the probability that fewer than 12 PC purchasers bought a Compaq?

e. What is the probability that exactly 22 PC purchasers bought a Compaq?