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?

Use the appropriate formula to answer the question: • Independent Probability: P(A and B) = P(A) x P(B) • Conditional Probability: P(A n B) = P(A) x P(B|A) • Addition Rule: P(A or B) = P(A) + P(B) – P(A and B) True or False: Events A and B are independent? P(A) = 0.60 P(B) = 0.70 P(A and B) = 0.42 True False

The​ three-year recidivism rate of parolees in a certain state is about 20​%; that​ is, 20​% of parolees end up back in prison within three years. Assume that whether one parolee returns to prison is independent of whether any of the others return. Complete parts a and b below.         Find the probability that exactly 6 out of 20 parolees will end up back in prison within three years.   The probability that exactly 6 out of 20 parolees will end up back in prison is nothing.

Here is a few scenarios where I want you to describe how you would set up either binomialcdf or binomialpdf on your calculators. Use correct probability notation (ex P(X = 3) = .1314), and for the inequalities give a brief example of which values for X you are trying to "include" in your calculation, and the logic behind why you are setting up your calculator function in a given way.  A Multiple Choice test is given consisting of 10 questions, each question having 5 possible answers, one of which is correct.  Jimmy hasn't studied and prepared himself for the test, and is therefore forced to completely guess on each question.  Find the probability that: (1) He gets exactly 5 (half) of the questions correct (2) He gets ALL the questions correct (3)  He gets NONE of the questions correct (4)  He gets at least a 60% (passing) on the test. (5)  He gets at most 5 correct.