The mean amount μ for all of the invoices for your company last month is not known. based on your past experience, you are willing to assume that the standard deviation of invoice amounts is about $250. if you take a random sample of 120 invoices, what is the value of the standard deviation for x? using the empirical rule, the probability is about 0.997 that x is within what amount of the population mean μ?

Aproduction line has three machines a, b, and c, with reliabilities of .96, .86, and .85, respectively. the machines are arranged so that if one breaks down, the others must shut down. engineers are weighing two alternative designs for increasing the line’s reliability. plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. in either case, three machines (a, b, and c) would be used with reliabilities equal to the original three. a. compute overall system reliability under plan 1. (round your intermediate calculations and final answer to 4 decimal places.) reliability b. compute overall system reliability under plan 2. (round your intermediate calculations and final answer to 4 decimal places.) reliability c. which plan will provide the higher reliability? plan2plan1