(2) Do the problem again this time using the normal approximation to the binomial distribution using the continuity correction A(2)_

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1 Computer Assignment 2 Due October 4, 2012 Solve the following problems using Minitab to do the calculations.attach the computer output but put your answers in the space provided Your computer output for this part should be your first page.. A. Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can he reworked (rather than having to be scrapped). Consider a random sample of shafts and let X denote the number among these that are nonconforming and can be reworked. (1) Find the exact probability that X is between 1080 and 1200 inclusive. MTB > cdf 1200 c1; SUBC> binomial MTB > cdf 1079 c2; SUBC> binomial MTB > let c3=c1-c2 MTB > print c3 C (2) Do the problem again this time using the normal approximation to the binomial distribution using the continuity correction A(2)_ MTB > cdf c4; MTB > cdf c5; MTB > let c6=c4-c5 MTB > print c6 C (3) Do the problem again this time using the normal approximation to the binomial distribution without the continuity correction.a(3). M Which of (2) and (3) give a better approximation to the exact value? MTB > cdf 1200 c7;

2 MTB > cdf 1079 c8; MTB > let c9=c7-c8 MTB > print c9 C MTB > The answer in (2) gives the better approximation. Your answer MTB > print c3 c6 c9 Row C3 C6 C Clearly the approximation that uses the continuity correction is better. B. Suppose that only.1% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 600,000 computers. (1) What is the expected value and standard deviation of the number of computers in the sample that fail during the warranty period? (Do this part by hand.) Write up your solution here Mean=600 Standard Deviation= (2) Using an appropriate binomial distribution find the probability that at most 610 sampled computers fail during the warranty period? MTB > cdf 610 c10; SUBC> binomial MTB > print c10 C (3) Using an appropriate Poisson distribution approximate the probability at most 610 sampled computers fail during the warranty period? (3) M MTB > cdf 610 c11;

3 SUBC> poisson 600. MTB > print c11 C (4) Use the normal approximation to the binomial distribution with the continuity correction to approximate the probability that at most 610 sampled computers fail during the warranty period? MTB > cdf c12; SUBC> normal MTB > print c12 C (5) Which approximation is more accurate? Row C10 C11 C Clearly the Poisson approximation is the better one. Your answer 2. Use Minitab to do this problem that demonstrates The Central Limit Theorem Do the computations in part A and answer the questions on page 2 stapled to the front of the computer output that should follow. A.This part is to be done by hand. You will use a exponential distribution with mean a where a is the number of letters in your last name. Thus, if you have 20 letters in your last name you will use f (x) = 1 20 e x / 20,x > 0 For your value of the parameter a find the mean and the standard deviation of the distribution by evaluating appropriate integrals. It will not suffice to substitute in the formulas below.put your final complete solution in the space below. Your last name is. The number of letters are Your integrations

4 For your value of a you should get an answer with numerical value a. You will now simulate your distribution 100 times. calc>randomdata>exponential In dialog box Generate 100 rows of data Store in columns c1-c100 Scale your value of a Threshold 0 OK enter the commands rmeans c1-c100 c101 Make a stem and leaf display for c50 using the pull down menu or the command stem-and-leaf c50 describe c50 Make a stem and leaf display for c101 using the pull down menu or the command stem-and-leaf c101 describe c101 Make normal probability plots for c50 and c101. Answer the following questions in the space provided.please attach the computer output. 1. Based on the stem and leaf display and the normal probability plot for c50 does the data appear to be normally distributed? Explain your answer. 2. Answer the same question for c101..

5 3. What is the mean and the standard deviation obtained in the describe command for c50 and c101? C50 mean = Standard Deviation Equals C101mean = Standard Deviation Equals 4. What should the mean and standard deviation be in theory for c50? for c 101?[Hint for c50 it should be what you got by integration in part A. For c101 the mean is the same and the standard deviation is divided by 10] In theory the mean is for c50 and c101 and the standard deviation is_ for c50 and 0.6 for c Compare the mean and standard Deviation in questions 3 and 4 by finding the percentage error? %error = 6. A. State the Central Limit Theorem carefully B. Explain how the results you obtain in c101 validates the central limit theorem for your problem.