Continuous Probability Distribution - Statistical Analysis
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JENN Inc. supplies under-hood emission control air pumps to the automotive industry. The pump is vacuum-powered and works while the engine is operating., cleaning the exhaust by pumping extra oxygen into the exhaust system. If a pump fails before the vehicle in which it is installed has travelled 50,000 miles, Federal emission regulations require that it be replaced at no cost to the vehicle owner. The company's current air pump lasts an average of 61,000 miles, with a standard deviation of 9,000 miles. The number of miles a pump operates before becoming ineffective has been found to follow a Normal distribution.
1. For the current pump design, what percentage of the company's pumps will have to be replaced at no charge to the vehicle owner? (show analysis for practice prob and show why)
2. What percentage of the company's pumps will fail at exactly 50,000 miles? (show analysis and why)
3. What percentage of the company's pumps will fail at mileage between 42,000 and 57,000 ? (show work/why)
4. For what number of miles does the probability become 80% that a randomly selected pump will no longer be effective? (show how assessed/why)
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Solution Summary
The solution calculates continuous probability distribution for JENN Inc.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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