David\'s gasoline station offers 4 cents off per gallon if the customer pays i c

Question

David's gasoline station offers 4 cents off per gallon if the customer pays i ca 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 14 What is the probability that at least ten pay in cash? A. 0.416 B.0575 D. 0.425 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 What is the probability that no more than twenty pay in cash? A. 0.0 B. 0.1 C.0.9 D. 1.0

Explanation / Answer

n = 25

p = 0.40

It is a binomial distribution.

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

14) P(X > 10) = 1 - P(X < 10)

                       = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9))

                       = 1 - (25C0 * (0.4)^0 * (0.6)^25 + 25C1 * (0.4)^1 * (0.6)^24 + 2521 * (0.4)^2 * (0.6)^23 + 25C3 * (0.4)^3 * (0.6)^22 + 25C4 * (0.4)^4 * (0.6)^21 + 25C5 * (0.4)^5 * (0.6)^20 + 25C6 * (0.4)^6 * (0.6)^19 + 25C7 * (0.4)^7 * (0.6)^18 + 25C8 * (0.4)^8 * (0.6)^17 + 25C9 * (0.4)^9 * (0.6)^16)

                     = 1 - 0.425

                    = 0.575

Option - B is correct

15) P(X < 20) = 1 - P(X > 20)

                      = 1 - (P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25))

                   = 1 - (25C21 * (0.4)^21 * (0.6)^4 + 25C22 * (0.4)^22 * (0.6)^3 + 25C23 * (0.4)^23 * (0.6)^2 + 25C24 * (0.4)^24 * (0.6)^1 + 25C25 * (0.4)^25 * (0.6)^0)

                 = 1 - 0.000008

                 = 0.9

Option - C

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