tpx value 10.00 points 31 percent of all customers who enter a store will make a

Question

tpx value 10.00 points 31 percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions (1) Use the binomial formula to calculate the probability that exactly five customers make a purchase (Round your answer to 4 decimal places) Probability (2) Use the binomial formula to calculate the probability that at least three customers make a purchase (Round your answer to 4 decimal places,) Probability (3) Use the binomial tormula Probability (4) Use the binomial formula to calculate the probability that at least one customer makes a purchase (Round your answer so Probability 0 0119 to calculate the probability that two or fewer customers make a purchase (Round your answer to 4 decimal places.) 4 decimal places.) References eBook & Resources Worksheet

Explanation / Answer

Please note nCx = n! / [(n-x)!*x!]

Binomial Probability = nCx * (p)x * (q)n-x, where n = number of trials and x is the number of successes.

Here n = 6, p = 0.31 and q = 1 - p = 1 - 0.31 = 0.69

(1) Exactly 5 make the purchase P(5) = 6C5 * (0.31)5 * (0.69)6-5 = 0.0119

(2) At least 3 make a purchase = P(3) + P(4) + P(5) + P(6)

P(3) = 6C5 * (0.31)3 * (0.69)6-3 = 0.1957

P(4) = 6C4 * (0.31)4 * (0.69)6-4 = 0.0659

P(5) = 6C5 * (0.31)5 * (0.69)6-5 = 0.0119

P(6) = 6C6 * (0.31)6 * (0.69)6-6 = 0.0009

The required probability = 0.1957 + 0.0659 + 0.0119 + 0.0009 = 0.2744

(3) 2 or fewer = P(0) + P(1) + P(2) = 1 - [P(3) + P(4) + P(5) + P(6) = 1 - 0.2744 = 0.7256

(4) At least 1 = P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1 - P(0)

P(0) = 6C0 * (0.31)0 * (0.69)6-0 = 0.1079

Therefore 1 - P(0) = 1 - 0.1079 = 0.8921

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.