The strength of manufactured crankshafts is a continuous random variable with the followingdistribution. According to the standard, a crankshaft is acceptable if its strength is larger than 2.ƒ(x) = { exp (− (5)²), x > 0a) Find the probability that more than 1 defective part is found in a sample of 50 producedcrankshafts.b) What is the average number of inspected crankshafts until 4 defectives are found?

The strength of manufactured crankshafts is a continuous random variable with the following…

Answered: The strength of manufactured…

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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The average number of miles (in thousands) that a car's tire will function before needing replacement is 65 and the standard deviation is 18. Suppose that 48 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 66.6 and 69.5. For the 48 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 66.6 and 69.5. For part d), is the assumption that the distribution is normal necessary?
Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?
Suppose the current measurements made on a conductor wire track follow a normal distribution with mean 10 milliamperes and variance 4 (milliamperes)^2 a) what is the probability that the value of a measurement is less than 9 milliamperes? b) what is the probability that the value of a measurement is greater than 13 milliamps? c) what is the probability that the value of a current measurement is between 9 and 11 milliamperes?
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The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 13. Suppose that 41 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 75 and 77.6. For the 41 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 75 and 77.6. For part d), is the assumption that the distribution is normal necessary? YesNo
The average number of miles (in thousands) that a car's tire will function before needing replacement is 67 and the standard deviation is 19. Suppose that 47 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 63 and 66.4. ? For the 47 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 63 and 66.4?
It is known that the average body temperature of healthy individuals is is normally distributed with a mean, μ = 37 oC and standard deviation, σ = 0.6 oC. We found the average temperature of a random sample of 24 University students in a Statistics tutorial. What is the probability that the average body temperature of this sample of students will be less than 37.1 oC? (4 dp) What is the probability that average body temperature of these students will be more than 37.4 oC?
2. A specially designed car tire has an average life of 38,500 miles with a standard deviation of 2,500 ms is approximately normally distributed. (a) Let X = number of miles of a single tire. Find the probability that in the sample above the mean will be less than 38,000 miles. (Use 4 decimals) rox< 38000) =nomacr (IEa, 3,0o, 38,500, 2,50).5442 PCX bobnpt.ou vnio (b) Use the software tool below (or any other) to graph and shade the probability from part (a). Do not graph manually. The graph should show the appropriate area from part (a). Tool link: https://mathcracker.com/normal-probability-calculator-sampling-distributions (c) The tire manufacturer wants to set the tire warranty to 39,100 miles. Is this a good decision? What are the possible consequences to the manufacturer? Explain in detail.
SAT scores in one state is normally distributed with a mean of 1496 and a standard deviation of 64. Suppose we randomly pick 43 SAT scores from that state. a) Find the probability that one of the scores in the sample is greater than 1503. P(X > 1503) = b) Find the probability that the average of the scores for the sample of 43 scores is greater than 1503. P(X > 1503) = Round each answer to at least 4 decimal places.

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