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 more than ten and less than fifteen customers pay in cash?
Click on the arrows to vote for the correct answer
A. B. C. D. E.E
Binomial distribution: n!(p^r)(q^(n-r))/r!(n-r)!. n = 25, r = 10, p = 0.4 q = 0.6
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
Summing up: 0.3799.