A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows: x < 0 0 0.04 0≤x<1 0.24 1 3) 5 ≤x≤6 6 ≤X (c) P(2 ≤x≤5)

Q6: Suppose that a shuttle’s launch depends on three key devices that operate independently of each other and malfunction with probabilities 0.01, 0.02 and 0.02, respectively. If any of the key devices malfunctions, the launch will be postponed. Compute the probability for the shuttle to be launched on time, according to its schedule?

A call center hires 10 call agents and owns 11 head sets for its call agents to use. Each call agent needs a head set. But the head sets are too old that they do not function well with a probability of 5%. Assume that the problem occurrence is inependent across head sets. Hint Use the following formulae Pr(X = x) = = n! = (2) p² (1 − p)²-² n! x!(n - x)! nx (n-1) x (n-2)xx2x1 and approximate (0.95)≈ 0.63, (0.95)¹0≈ 0.60 and (0.95)¹¹ ≈ 0.57. (a) Let X be the number of head sets functioning well. What are the parameters for the binomial distribution for X? (b) Calculate the expected number of head sets that function well. Do you think that the call center has enough head sets? (c) Calculate the probability that only one head set is not functioning well (d) Calculate the probability that 10 head sets or more are functioning well. (e) Calculate the probability that there are NOT enough functioning head sets. (f) Suppose that a head set is lost. Now only 10 head sets are available. Calculate…

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