The mean time between failures (MTBF) is a common metric used to measure the performance of manufacturing systems. MTBF is the elapsed time between failures of a system during normal operations. The failures could be caused by broken machines or computer errors, among other failures. Suppose that the MTBF for a new automated manufacturing system follows an exponential distribution with a mean of 12.2 hours. (a) What is the probability that the automated manufacturing system runs for more than 18 hours without a failure

Asample of 200 rom computer chips was selected on each of 30 consecutive days, and the number of nonconforming chips on each day was as follows: the data has been given so that it can be copied into r as a vector. non.conforming = c(10, 15, 21, 19, 34, 16, 5, 24, 8, 21, 32, 14, 14, 19, 18, 20, 12, 23, 10, 19, 20, 18, 13, 26, 33, 14, 12, 21, 12, 27) #construct a p chart by using the following code. you will need to enter your values for pbar, lcl and ucl. pbar = lcl = ucl = plot(non.conforming/200, ylim = c(0,.5)) abline(h = pbar, lty = 2) abline(h = lcl, lty = 3) abline(h = ucl, lty = 3)

Write each rational number in the form a/b, where a and b are integers. 1. 5 1/6 2. -12

Arandom sample of size n 64 is taken from a population with population proportion p 0.38 describe the sampling distribution of p. draw a graph of this probability distribution with its a. mean and standard deviation. b. what is the probability that the sample proportion is greater than 0.5? what is the probability that the sample proportion is less than 0.3? d. what is the probability that the sample proportion is between 0.35 and 0.45?