A call center hires 10 call agents and owns 11 head sets for its call agents to use. Each call agent needs a headset. But the head sets are too old that they do not function well with a probability of 5%. Assume that the problemoccurrence is inependent across head sets.Hint Use the following formulaePr(X = x)==n! =(2) p² (1 − p)²-²n!x!(n - x)!nx (n-1) x (n-2)xx2x1and 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 forX?(b) Calculate the expected number of head sets that function well. Do you think that the call center hasenough 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 thatthere are enough functioning head sets. How much does this probability change due to the loss of ahead set?

A call center hires 10 call agents and owns 11 headsets.The headsets do not function well with a…

Answered: A call center hires 10 call agents and…

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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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.
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
Suppose that you repeatedly roll a pair of fair dice and keep track of the sum. What is the probability that you see a sum of 7 before you see an even sum 3 times? (In particular, you keep track of how many evens you roll, and you want the probability that you roll a 7 before you get to 3 evens.
A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.050.05. On visiting a holiday resort for seniors, he sells 1010 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 1010 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places.Part a)What is the expected number of policies that will pay out before the insured parties have reached age 61?Part b)What is the variance of the number of policies that will pay out before the insured parties have reached age 61?Part c)What is the probability that at least two policies will pay out before the insured parties have reached age 61?
Please provide steps for how you got the solution to the problem provided below. A machine is used to produce one of each of two types of product (A and B) on alternating days, i.e., if A is produced today then B will be produced tomorrow and vice versa. Each day, there is a probability that the machine malfunctions. Malfunction probability after a day of operation is 0.03 when producing A and 0.07 when producing B. Once the machine malfunctions, it is no longer operable and will not be replaced until sometime in the future (beyond modeling horizon). Model the system as a Markov chain (give transition matrix on your paper). Suppose that on Monday product A was produced. Find the probability that the machine is still operable by the morning of Thursday. Your model should have a state ”malfunction”, which cannot transition to any other state other than itself.
The probability that Mr. Johnson goes for an evening walk on any given day during the winter is 0.56. Out of 89 days of winter, the number of days that Mr. Johnson is expected not to take an evening walk to the nearest day, is

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