The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.1 mm.(a) What is the probability that defect length is at most 20 mm? Less than 20 mm? (Round your answers to four decimal places.)at most 20mm0.1299less than 20mm0.1024(b) What is the 75th percentile of the defect length distribution-that is, the value that separates the smallest 75% of all lengths from the largest 25%? (Round your answer to three decimal places.)32.789mm(c) What is the 15th percentile of the defect length distribution? (Round your answer to three decimal places.)20.6413(d) What values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%? (Round your answers to three decimal places.)smallest 10%mmlargest 10%mmYou may need to use the appropriate table in the Appendix of Tables to answer this question.

a) At most 20 mm means less than or equal to 20. Less than 20 mm means X<20. For normal…

Answered: The defect length of a corrosion defect…

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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The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 65 with a standard deviation of 10. Assume that the distribution is approximately normal. (a) What is the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg? answer: (b) What is the probability that an elite athlete has a maximum oxygen uptake of 60 ml/kg or lower? answer: (c) Consider someone with a maximum oxygen uptake of 31 ml/kg. Is it likely that this person is an elite athlete? Write "YES" or "NO." answer:
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
The lifetime of a lightbulb in a certain application is normally distributed with mean μ = 1,500 hours and standard deviation σ = 200 hours. 1. What is the probability that a lightbulb will last more than 1800 hours? (Round the final answer to four decimal places.) 2. Find the 10th percentile of the lifetimes. (Round the final answer to the nearest integer.) 3. A particular lightbulb lasts 1645 hours. What percentile is its lifetime on? (Round the final answer to the nearest whole number.)
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr
On average, indoor cats live to 12 years old with a standard deviation of 2.4 years. Suppose that the distribution is normal. Let X = the age at death of a randomly selected indoor cat. Round answers to 4 decimal places where possible. %3D a. What is the distribution of X? X N( b. Find the probability that an indoor cat dies when it is between 12.7 and 15.6 years old. c. The middle 50% of indoor cats' age of death lies between what two numbers? Low: years High: years Hint:
Scores on a standardized exam are known to follow a normal distribution with standard deviation σ = 21. A researcher randomly selects 125 students and computes their average score. He reports that the mean score is 73.8, with a margin of error of 2.920. How confident are you that the mean score for all students taking the exam is in the interval (70.88, 76.72)?
Assume that females have pulse rates that are normally distributed with a mean of μ=74.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts (a) through (c) below. Question content area bottom Part 1 a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 67 beats per minute and 81 beats per minute. The probability is 0.42450.4245. (Round to four decimal places as needed.) Part 2 b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 67 beats per minute and 81 beats per minute. The probability is enter your response here. (Round to four decimal places as needed.)

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