1) The length of time, Y, that a customer spends in line at a bank teller's window before being served is described by the exponential pdf:
f(y) = 0.2e-0.2y, y ³ 0.
a) What is the probability that a customer will wait for more than 10 minutes?
I used 1 - P( Y £ 10 ) = 1 - 0.2e-0.2y = 0.9729
b) Suppose the customer will leave if the wait is more than 10 minutes. Assume that the customer goes to the bank 3 times next month. Let the random variable X be the number of times the customer leaves without being served. Find P(X=1).
This I'm not sure how to do. Any hints?
2) A warehouse contains 10 printing machines, 3 of which are defective. A company selects 5 of the machines at random. What is the mean number of defective printers selected?
Since there are 3 defective machines, I found the probability of picking each one.
Then I multiplied the number of the defective machine by its probability of being selected and summed them all up: (3/10) + [2*(2/9)] + [3*(1/8)] = 1.1194
Does this seem right?