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 = 2.8 and = 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 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) (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.)

Grade inflation 2012. In 1996, 20% of the students at amajor university had an overall grade point average of 3.5or higher (on a scale of 4.0). In 2012, a random sample of1100 student records found that 25% had a GPA of 3.5 orhigher. Is this evidence of grade inflation?

o bag the potato chips. They had noticed a wide variability in th ags that were being produced with their current equipment, and e the variability. Therefore, they decided to determine if a newer reduce the variability in the weights of the bags. They randomly gs from their current machine and 50 bags from the new machin ded an average weight of 10 ounces. However, the current mach tion of 0.15 ounces and the new machine had a standard deviatic es.Carry out the appropriate hypothesis test at the a = 0.05 lev ..

The lifetime T (in years) for a particular type of electric toothbrush is assumed to have the probability density f given by t 0 ≤ t ≤6 f(t) = {+ 3 18 otherwise.

QUESTION 4 The time to failure of a typical household refrigerator has the following PDF Jo.000192t2 for 0sts 25 yr f(t) elsewhere Find: a. R(15) b. Construct the hazard rate function c. What is the probability that a failure will occur between the second and the tenth year? d. What is the MTTF? Attach File Browse Local Files Browse Content Collection

Product failure behavior. An article in Hotwire (Dec. 2002) discussed the length of time till failure of a product pro- duced at Hewlett-Packard. At the end of the product’s life- time, the time till failure is modeled using an exponential distribution with mean 500 thousand hours. In reliability jargon, this is known as the “wear-out” distribution for the product. During its normal (useful) life, assume the prod- uct’s time till failure is uniformly distributed over the range 100 thousand to 1 million hours.   a. At the end of the product’s lifetime, find the probability that the product fails before 700 thousand hours.   b. During its normal (useful) life, find the probability that the product fails before 700 thousand hours.   c. Show that the probability of the product failing before 830 thousand hours is approximately the same for both the normal (useful) life distribution and the wear-out distribution

The week before the bill to repeal Obamacare came up for consideration in the Senate, one polling agency increased the size of the random sample of U.S. adults they surveyed on this issue from 500 to 1500. What effect would this increase have on the polling agency's estimate of the proportion of U.S. adults in favor of repealing Obamacare, assuming the true proportion in favor remained constant? (A) A reduction in the variability of the estimate (B) An increase in the variability of the estimate (C) A reduction in the bias of the estimate (D) An increase in the bias of the estimate (E) A reduction in both the variability and the bias of the estimate

Question 5: A test engineer discovered that the cumulative distribution function of the lifetime of an equipment (in years) is given by Fx(x)= 1-e VS), x20. What is the expected lifetime of the equipment? 直。

An article suggests the lognormal distribution as a model for SO2 concentration above a certain forest. Suppose the parameter values are μ = 1.7 and σ = 1.2. (a) What are the mean value and standard deviation of concentration? (Round your answers to three decimal places.)   (b) What is the probability that concentration is at most 10? Between 5 and 10?

2 The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 250 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.02? (Round your answer to two decimal places.) cfs