Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
SMAM 314 Worksheet 2 Name______________ 1. Consider the discrete probability mass function x 1 2 3 4 f(x) .1 .2 .3 .4 Find A. P[2 ≤ X ≤ 4] B. P[X = 1.5] C. The mean and the variance of X. D. The cumulative distribution function of X 2. The phone lines to an airline reservation system are occupied 45% of the time. Assume the events that the lines are occupied on successive calls are independent. Suppose seven calls are placed to the airline. A. What is the probability the lines are occupied for exactly four calls? B. What is the probability the lines are occupied for at most two calls? 3. Messages arrive at a computer server according to a Poisson distribution with a mean rate of 5 per hour. A. What is the probability that at least three messages will arrive in an hour? B. What is the probability that exactly seven messages will arrive during two hours? C. What is the probability that the time between two messages will be at most 10 minutes? 4. The manufacturing of semiconductor chips produces 3% defective chips. Assume that the chips are independent and that a lot contains 2000 chips. Use the normal approximation to the binomial distribution with the continuity correction to approximate the probability that a lot has at least 65 defective chips. 5. A synthetic fiber that is used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 4.5 psi. Find the probability that a random sample of n = 9 fiber specimens will have a sample mean tensile strength that exceeds 76.8 psi 6. A cartridge company develops ink cartridges for a printer company and supplies both the ink and the cartridges. The following is the probability mass function of the number of Cartridges used during the life of a printer. x 5 6 7 8 9 g(x) .04 .19 .61 .13 .03 A. What is the probability that for seven randomly selected printers at least five use more than seven cartridges during their life? B. Consider a random sample of 100 printers. Using the central limit theorem approximate the probability that a total of at least 710 cartridges are needed?