You believe that the vending machine in Allgood Hall will eat (accept but not cr
ID: 3305612 • Letter: Y
Question
You believe that the vending machine in Allgood Hall will eat (accept but not credit or return) any given dollar you try to use with probability .01. If, in the course of a year, you try to use 75 $1 bills in the machine, what is the probability....
..that it will eat two or more of them. Assume each dollar you use is independent.
...it will eat none of them.
...it will eat exactly three of them.
If X = the number of these 75 bills eaten by the machine, find the mean and standard deviation of X.
mean of X = bills
st. dev of X = bills
Explanation / Answer
This is a case of binomial distribution, with n = 75
p = 0.01 and
q = 0.99
P(eating 2 or more) = 1 - P(eating less than 2)
= 1 - P(0) - P(1)
= 1 - 0.9975 - 75x0.01x0.9974
= 1 - 0.4706 - 0.3565
= 0.1729
P(eating none of them) = P(0) = 0.4706
P(eating exactly three of them = 75C3 x 0.013 x 0.9972
= 0.03275
Mean of X = np = 75x0.01 = 0.75
Variance = npq = 75x0.01x0.99 = 0.7425
Standard deviation = sq root(variance) = 0.8617
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