Question

Steele Electronics Inc. sells expensive brands of stereo equipment in several shopping malls. The marketing research department of Steele reports that 35% of the customers entering the store that indicate they are browsing will, in the end, make a purchase. Let the last 20 customers who enter the store be a sample.

a. How many of these customers would you expect to make a purchase? (Round the final answer to the nearest whole number.)

Number of Customers            

b. What is the probability that exactly six of these customers make a purchase? (Round the final answer to 4 decimal places.)

Probability            

c. What is the probability 11 or more make a purchase? (Round the final answer to 4 decimal places.)

Probability            

d. Does it seem likely at least one will make a purchase ("likely" refers if the probability is more than 70%)?

(Click to select)  Yes  No

Answer 1

a) n = 20

    p = 0.35

Expected value = np = 20 * 0.35 = 7

b) P(X = x) = nC x * p^x * (1 - p)^{n - x}

P(X = 6) = 20C6 * (0.35)^6 * (0.65)^14 = 0.1712

c) P(X > 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(x = 20)

= 20C11 * (0.35)^11 * (0.65)^9 + 20C12 * (0.35)^12 * (0.65)^8 + 20C13 * (0.35)^13 * (0.65)^7 + 20C14 * (0.35)^14 * (0.65)^6 + 20C15 * (0.35)^15 * (0.65)^5 + 20C16 * (0.35)^16 * (0.65)^4 + 20C17 * (0.35)^17 * (0.65)^3 + 20C18 * (0.35)^18 * (0.65)^2 + 20C19 * (0.35)^19 * (0.65)^1 + 20C20 * (0.35)^20 * (0.65)^0 = 0.0532

d) P(X > 1) = 1 - P(X < 1)

                 = 1 - P(X = 0)

                 = 1 - (20C0 * (0.35)^0 * (0.65)^20)

                 = 1 - 0.0002

                = 0.9998

Since the probability is greater than 0.70, so it is likely at least one will make a purchase.