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Let X be the time it takes a bank customer to use an ATM machine. Suppose X has an exponential distribution with mean three minutes.

Let X be the time it takes a bank customer to use an ATM machine. Suppose X has an exponential distribution with mean three minutes. The Bank has to pay C = 10 + 2X + X2 (in cents) to operate the machine for X minutes. (a) Find the expected value of C. (b) Find the probability that the bank will have to spend more than 30 cent to operate the ATM machine for the next customer. (Hint: google "quadratic formula" if you forgot it from your Calculus class)

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