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:F(X) =(b)Calculate the following probabilities directly from the cdf:(a) p(2), that is, P(X = 2)(c)0x < 00.040 ≤ x < 10.24 1 3)P(2 ≤x≤5)P(2 < X <5)

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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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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: F(x) = (b) Calculate the following probabilities directly from the cdf: (a) p(2), that is, P(X = 2) (c) 0 0.09 0.21 0.33 0.53 0.90 0.99 1 P(X > 3) x < 0 0 < x < 1 1 ≤ x < 2 2
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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)