Answered: 4. The owner of a tree farm specializes… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 27T

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4.4 give the probability data analysis, show solution.

4. The owner of a tree farm specializes in growing pine trees. They are grown in rows of
50 trees and the owner has found on the average, about 4 trees per row will not be
suitable to sell. Assuming that the Poisson distribution is applicable here, find the
probability that a row of tree selected for shipment will contain 2 unsaleable trees.

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Suppose the number of errors logged on a network follows a Poisson distribution. The mean time between errors is 4 minutes. Answer the following questions. a) Find the probability the wait time until the next error is logged is more than 3 minutes. b) Find the probability the wait time until the next error is logged is less than 45 seconds. c) Find the probability the wait time until the next error is logged is between 3 minutes and 5 minutes.
On average, there is one hurricane in the Bahamas every year. The cost torepair the damage of each hurricane in the Bahamas to a particular resort is 100. To stabilizefinances, the resort buys hurricane insurance, which will cover the cost of the repairs foreach hurricane after the second. Assume that the number of hurricanes in the Bahamas ina given year is Poisson distributed. 1. What is the expected cost of repairs in a given year to the resort (not including thecost of insurance)?2. What is the expected payout of the insurance company on the resort’s policy in agiven year?
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st
12. Normally distributed data are referred to as:
If one sample with a mean of M = 10 is combined with a second sample with a mean of M = 20, then the mean for the combined sample will be between 10 and 20. True False
1. The numbers of customers who patronise a coffee shop follow Poisson distribution with mean of 20 per hour. Find the probability that: a) No customer patronises the coffee shop in a time interval of 6 minutes. b) At least one customer patronises the coffee shop in a time interval of 12 minutes. c) Between 2 and 4 customer patronises the coffee shop in a time interval of 12 minutes. 2. The number of telephone calls received by an operator follows a Poisson distribution with mean 4. Find the probability that: a) The operator will not receive any call. b) The operator will receive a total of 3 calls. 3. Cars arriving at a toll at an average rate of 30 per hour. Assuming the number of cars arriving at the toll follows a Poisson distribution, find the probability that a) No car arrives during a particular 5-minute interval b) At most two cars arriving during a particular 10-minute interval c) More than four cars arriving during a 15-minute interval 4. A receptionist in a…
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2
The Johnson & Johnson Company operates 6 identical machines that are serviced by a single technician when they breakdown. These breakdowns occur according to the Poisson distribution and average 0.03 breakdowns per machine operating hour. Average repair time for a machine is 5 hours and follows the exponential distribution. a) What percent of the technician's time is spent repairing machines? Answer in 4 decimal places. Blank 1 b) On average, how long is a machine out of service because of a breakdown? Answer in 2 decimal places. Blank 2 c) On average, how many machines are out of service? Answer in 1 decimal place. Blank 3 Blank 1 Blank 2 Blank 3 Add your answer Add your answer Add your answer
2. Doctors volunteer their time on a daily basis in a clinic. The total number of patients served in a day at the clinic has mean 90 and variance 1890. Determine the probability that 120 or more patients can be served in a day at the clinic. Use the Central Limit Theorem with continuity correction. Use linear interpolation with the normal distribution to find the probability.
Suppose that the length of research papers is uniformly distributed from 10 to 25 pages. We survey a class in which 55 research papers were turned in to a professor. The 55 research papers are considered a random collection of all papers. We are interested in the average length of the research papers. Why is it so unlikely that the average length of the papers will be less than 12 pages?

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