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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An experiment is conducted to compare the maximum load capacity in tons (the maximum weight that can be tolerated without breaking) for two alloys A and B It is Kknown that the two standard deviations in load capacity are equal at 7 tons each. The experiment is conducted on 50 specimens of each alloy (A and B) and the results are X = 75.8. X = 71.8, and X-X=4. The manufacturers of alloy A are convinced that this evidence shows conclusively that Hug and strongly supports the claim that their alloy is superior. Manufacturers of alloy 8 claim that the experiment could easily have given X-X 4 even if the two population means are equal. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA-XB41 PA-HB) P(XA-X > 4) - @
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
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
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in thedusLove uo useful life (150,000 miles of driving) of cars of a particular model varies Normall/ih nean 80 mg/mi and standard deviation 4 mg/mi. A company has 25 cars of this model in its et find the level L such that the probability that the average NOX+NMOG level 7 for the fleet is greater than L is only 0.01. Give your answer to three decimal places.
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=| S= (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…
Solve question 9, Part A, Part B and Part C only.
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 20 days and a standard deviation of 5 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.
The time spent (in days) waiting for a heart transplant in two states for patients with type A+ blood can be approximated by a normal distribution, as shown in the graph to the right. Complete parts (a) and (b) below. u= 134 0=18.1 What is the shortest time spent waiting for a heart that would still place a patient in the top 30% of waiting times?

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