solve these probability problems
The Murphy County Fire Department is consider- ing two options for upgrading its aging physical fa- cilities. Plan A involves remodeling the fire stations on Alameda Avenue and Trowbridge Boulevard that are 57 and 61 years old, respectively. (The industry standard is about 50 years of use for a station.) The cost for remodeling the Alameda station is esti- mated at $952,000 while the cost of redoing the Trowbridge station is $1.3 million. Plan B calls for buying 5 acres of land somewhere between the two stations, building a new fire station, and selling the land and structures at the previous sites. The cost of land in that area is estimated to be $366,000 per acre. The size of the new fire station would be 9000 square feet with a construction cost of $151.18 per square foot. Contractor fees for overhead, profit, etc. are expected to be $140,000, and architect fees will be $81,500. (Assume all of the costs for plan B occur at time 0.) If plan A is adopted, the extra cost for personnel and equipment will be $126,000 per year. Under plan B, the sale of the old sites is antici- pated to net a positive $500,000 five years in the future. Use an interest rate of 6% per year and a 50- year useful life for the remodeled and new stations to determine which plan is better on the basis of a present worth analysis.The time to failure in hours of an important piece of electronic equipment used in a manufactured DVD player has the density function /(z) = zin exp(-2/2000), 2 2 0. I CO. (3) Find F(x).(b) Determine the probability that the component (and thus the DVD player) lasts more than 1000 hours before the component needs to be replaced (b) Determine the probability that the component fails before 2000 hours. A manufacturer of electronic components is interested in determining the lifetime of a certain typeof battery. A sample, in hours of life, is as follows: 123, 116, 122, 110, 175, 126, 125, 111, 118, 117. (a) Find the sample mean and median. (b) What feature in this data set is responsible for the substantial difference between the two?The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function 20.000 f(x) = (x+100) I>0, 0 , elsewhere. Find the probability that a bottle of this medicine will have a shell life of (a) at least 200 days; (b) anywhere from 80 to 120 days.Assume an engineering company borrows $100,000 at 10% per year compound interest and will pay the principal and all the interest after 3 years. Compute the annual interest and total amount due after 3 years. Graph the interest and total owed for each year, and compare with the previous example that involved simple interest.\f
