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# Calculating Probability of Purchases

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Historically, 70% of your customers at Rodale Emporium pay for their purchases using credit cars. In a sample of 20 customers, find the probability that

a. Exactly 14 customers will pay for their purchases using credit cards.
b. At least 10 customers will pay for their purchases using credit cards.
c. At most 12 customers will pay for their purchases using credit cards.

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#### Solution Summary

This solution is comprised of a detailed explanation for calculating the probabilities using Binomial distribution. All questions are answered using the binomial distribution with the help of binomial table to find the probabilities. The detailed solution is provided for better understanding.

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## Calculating optimal purchase amount.

The probability distribution for the demand of a product has been estimated to be:

Demand Probability of Demand
0 0.05
1 0.15
2 0.30
3 0.35
4 0.10
5 0.05
6 0.00
1.00

Each unit is purchased for \$10 and each unit sells for \$50. Unsold units are worthless (no scrap value).

How many units should be purchased if no reordering is possible?

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