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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 = 1) (C) n! = nx (n-1) x (n-2)xx 2x1 (*)p²(1 − p)"-² n! x!(n-x)! = 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 the probability that there are enough functioning head sets. How much does this probability change due to the loss of a head set?

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 = 1) (C) n! = nx (n-1) x (n-2)xx 2x1 (*)p²(1 − p)"-² n! x!(n-x)! = 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 the probability that there are enough functioning head sets. How much does this probability change due to the loss of a head set?

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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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 the probability that there are enough functioning head sets. How much does this probability change due to the loss of a head set?
Transcribed Image Text: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 the probability that there are enough functioning head sets. How much does this probability change due to the loss of a head set?
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