sales firm receives, on average, 3 calls per hour on its toll-free number. For any given hour, find the probability that it will receive the following using the Poisson table. (a) At most 3 calls
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4. A sales firm receives, on average, 3 calls per hour on its toll-free number. For any given hour, find the probability that it will receive the following using the Poisson table. (a) At most 3 calls
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- 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.A certain tennis player makes a successful first serve 78% of the time. Assume that each serve is independent of the others. If she serves 9times, what's the probability she gets: Part 1 a) The probability that she gets all 9 serves in is _______________ (Round to three decimal places as needed.). Part 2 b) The probability she gets exactly 4 serves in is _______________ (Round to three decimal places as needed.) Part 3 c) The probability she gets at least 7 serves in is ______________________ (Round to three decimal places as needed.) Part 4 d) The probability that there are no more than 6 serves in is __________ (Round to three decimal places as needed.)A local company has two identical lathe machines which are operated independently. A log is kept for each of the two machines and Table QII below shows the number of times that each machine has been operational in the last twelve months. Lathe Status Number of times working Number of times not working A B 780 650 220 350 Table QII Draw the probability tree diagram and solve following questions Q1 If two machines are dependent what is the probability of either lathe working at the visit of supervisor? Q2 What is the probability that only one lathe would broke down? Q3 What is the probability that at least one lathe would have broken down ?
- 1) A manufacturer will purchase a battery from one of two suppliers. This manufacturer will get the battery from supplier 1 with probability 0.6 and from supplier 2 with probability 0.4. A battery obtained from supplier 1 has a lifetime, which is exponentially distributed with a mean of 6 months. On the other hand, the lifetime of a battery from supplier 2 is again exponentially distributed with a mean of 5 months. What is the probability that the purchased battery (from supplier 1 or 2 with aforementioned probabilities) will last more than 5 months?Given P(A) = 0.10, P(B) = 0.63, P(C) = 0.53 and that events A, B, and C are independent, what is P(A, B, and C). Answer in decimal form. Round to 3 decimal places as needed.Suppose that we perform an experiment where we classify the outcome as either a success or a failure. Let the probability of a success be 0.90.9 . Now we want to repeat this experiment n = 44 times and let the random variable X count the number of successes. Visualize a probability tree for this situation (without actually drawing it out). Round to four decimal places as needed. From each vertex there will be 22 edges going to a success S and a failure F. Since each stage is independent all the edges going to an S will have probability p = . 9.9 and all the edges going to an F will have probability q = . 10.10. If a single path has 2 success and the rest failures (in any order) then the probability of that single path is nothing. Note that these 2 successes may be in any of the 44 stages so there are nothingof these paths which have 2 successes. Therefore, P(X = 2) = nothing.
- Suppose the weather moves between three states 1,2,3. It stays in state 1 for an exponentially distributed number of days with mean 3, then goes to state 2. It stays in state 2 for an exponentially distributed number of days with mean 4, then goes to state 3. It stays in state 3 for an exponentially distributed number of days with mean 1, then goes to state 1. Compute the long-term probability that the weather is in state 1. Write your answer as a decimal.zample 3: Alexis is selling girl scout cookies. She has kept track of the number of boxes of cookies at her customers have purchased over the last 2 years. She wants to use this data to help edict how many boxes of cookies a new customer might purchase. The table below summarizes exis' data, with the number of boxes that a customer might purchase along with the rresponding probability that they will purchase that number of boxes based on her previous les. Use this information to answer the following questions. Outcomes: 2 3 4 5 6 7 8 X = x Probability: P(X = x¡) 0.21 0.16 0.32 0.11 0.08 0.05 0.04 0.02 0.01 a) Construct a probability histogram of the data in the table above and comment on the shape. ) What is the probability that a randomly selected customer will purchase 3 boxes of cookies? What is the probability that a randomly selected customer will purchase at least 4 boxes of cookies? What is the probability that a randomly selected customer will purchase anywhere from 2 to 5…Q5. It was found that a New Brunswick family doctor has on average 14 patients calling in for anappointment they say they need to have on that very day during a standard 10 hour work day.Using the tables(a) What is the probability that a New Brunswick family doctor has more than 20 patientscalling in for an appointment they say they need to have on that very day during a standard10 hour work day?(b) What is the probability that a New Brunswick family doctor has more than 2 patientscalling in for an appointment they say they need to have on that very day during the nexthour?(c) What is the probability that a New Brunswick family doctor has 7 or less 20 patientscalling in for an appointment they say they need to have on that very day during the next3 hours?(d) For this situation, determine the probabilities of being within 1, 2 an d 3 standard deviations for the mean and compare these results to the empirical rule