The optimal scheduling of preventive maintenance tests of some (but not all) of n independently operating components was developed in Reliability Engineering and System Safety (January 2006). The time (in hours) between failures of a component was approximated by an exponential distribution with mean θ. Suppose θ = 1000 hours. Given that the time between failures is at least 1,500 hours, what is the probability that the time between failures is less than 2,000 hours?

An economist studying inflation in electricity prices in 2018 and 2019 believes that the average price of electricity, even after adjusting for inflation, changed between these two years. To test his claim, he samples 9 different counties and records the average price of electricity in each county from each year. He then adjusts the prices for inflation. His results are given in the following table. Test the economist’s claim at the 0.10 level of significance assuming that the population distribution of the paired differences is approximately normal. Let prices in 2018 be Population 1 and prices in 2019 be Population 2.  Average Residential Retail Prices of Electricity ($/kWh) 2018 2019 19.99 18.65 15.30 17.29 14.40 16.17 17.31 18.68 12.85 13.53 12.41 13.11 14.74 13.13 19.15 19.36 11.84 13.69   Step 3 of 3 :   Draw a conclusion and interpret the decision.   1. We fail to reject the null hypothesis and conclude that there is insufficent evidence at a…

The incubation time for a breed of chicks is normally distributed with a mean of 29 days and standard deviation of approximately 3 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) (a) in 23 to 35 days __ chicks(b) in 26 to 32 days  __chicks

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