CFA Level 1: Probability of Cash Payments at David's Gasoline Station

Probability of At Least Ten Customers Paying in Cash

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Question

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twenty-five customers buy gasoline at this station. What is the probability that at least ten pay in cash?

Answers

Explanations

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A. B. C. D. E.

B

This is a binomial distribution: n!(p^r)(q^(n-r))/r!(n-r)!. n = 25, r = 10, p = 0.4 q = 0.6

P(10) = 25!(0.4^10)(0.6^15)/10!15! = 0.1612

P(11) = 25!(0.4^11)(0.6^14)/11!14! = 0.1465

P(12) = 25!(0.4^12)(0.6^13)/12!13! = 0.1140

P(13) = 25!(0.4^13)(0.6^12)/13!12! = 0.0760

P(14) = 25!(0.4^14)(0.6^11)/14!11! = 0.0434

P(15) = 25!(0.4^15)(0.6^10)/15!10! = 0.0212

P(16) = 25!(0.4^16)(0.6^9)/16!9! = 0.0088

P(17) = 25!(0.4^17)(0.6^8)/17!8! = 0.0031

Summing up we get close to 0.574.

We can continue until r = 25 but the probability gets smaller and converges to 0.575.

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