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A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is .1. Define a random variable X to be the number of machines that will break down in a day.

a. what is the appropriate probability distribution for X? Explain how X saisfies the properties of the distribution.
b. compute the probability that 4 machines will break down.
c. compute the probability that at least 4 machines will break down.
d. what is the expected umber of machines that will break down in a day?
e. What is the variance of the number of machines that will break down in a day?

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