3. (21 pts) 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 satisfies 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 number of machines that will break down in a day