38 percent of all customers who enter a store will make a purchase. Suppose that

Question

38 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. Probability (2) Use the binomial formula to calculate the probability that at least three customers make a purchase. Probability (3) Use the binomial formula to calculate the probability that two or fewer customers make a purchase. Probability (4) Use the binomial formula to calculate the probability that at least one customer makes a purchase. Probability

Explanation / Answer

Let X denote the number of customers that make a purchase.

Here success probability p = 0.38

(1)

P(X=1) = 6C5.p5.(1-p)6-5 = 6*0.385*0.621 = 0.029

(2)

P(X>=3) = 1 - ( P(X=0) + P(X=1) + P(X=2) )

P(X=0) =  6C0.p0.(1-p)6 = 1*0.380*0.626 = 0.0568

P(X=1) =  6C1.p1.(1-p)6-1 = 6*0.381*0.625 = 0.208

P(X=2) =  6C2.p2.(1-p)6-2 = 15*0.382*0.624 = 0.32

So,

P(X>=1) = 1 - (0.0568+0.208+0.32) = 0.4152

(3)

P(X<=2) = P(X=0) + P(X=1) + P(X=2)

From above part, we get:

P(X<=2) = 0.0568+0.208+0.32 = 0.5848

(4)

P(X>=1) = 1 - P(X=0)

P(X=0) =  6C0.p0.(1-p)6 = 1*0.380*0.626 = 0.0568

So,

P(X>=1) = 1 - 0.0568 = 0.9432

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