Question

Thirty percent (30%) 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. Let x be the number of the 6 customers who will make a purchase.

Use the binomial formula to calculate

- The probability that exactly 2 customers make a purchase.
- The probability that 2 or fewer customers make a purchase.
- The probability that at least 1 customer makes a purchase

Answer #1

Answer: Thirty percent (30%) 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. Let x be the number of the 6 customers who will make a purchase.

Solution:

X ~ Bin(6, 0.30)

Using the binomial distribution,

P(X = x) = nCx * p^x * (1-p)^n-x

**Therefore,**

**The probability that exactly 2 customers make a purchase
= 0.3241**

**The probability that 2 or fewer customers make a
purchase = 0.7743**

**The probability that at least 1 customer makes a
purchase = 0.8823**

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