Probability and Statistic for Engineer and Scientist - Solution for Exam 2 | STAT 4705, Exams of Statistics

Download Probability and Statistic for Engineer and Scientist - Solution for Exam 2 | STAT 4705 and more Exams Statistics in PDF only on Docsity! STAT 4705 Spring 2009 Probability & Statistics for Engineers & Scientists Virginia Tech University Score:_______ total Exam Two Please read the following directions carefully. Failure to follow directions may result in loss of points or your exam not being graded at all. DIRECTIONS: 1. Please direct all questions concerning this exam only to the instructor. Do not collaborate with a student in the classroom during the exam. 2. For each problem involving a calculation, circle your final answer. Remember to show as much work as possible so that you get the maximum credit allowed. 3. When you finish your exam, print your name at the bottom of this cover sheet and sign the honor pledge. Submit the entire exam booklet to the instructor. 4. Do not cheat on this exam. 5. Please turn off (not on vibrate) all cellular phones and pagers before opening this booklet. If your phone or pager rings or vibrates during the examination where it disturbs your classmates (or comes to the attention of the instructor), you will receive a grade of zero. 6. Turn in your formulas sheet with the exam. I agree to take the exam under the above directions, and have completed this exam in compliance with the Virginia Tech University Honor Code. ___________________________________________ _____________________ Signature Date ___________________________________________ Print your name. 1 Problem 1 (5+5+5 =15p) A chemical reacts in a process with probability 0.35. You run 150 independent trials of this process. Let X be the number of times the chemical reacts. a) Describe the distribution of X. (Give the name of the distribution and the mean and variance) b) What’s the probability that the chemical reacts in less than 40 of the processes? (Work the problem until a reasonable format of the final answer, meaning you don’t need to get a final numerical answer for the summation with a large number of terms). c) Give a second method you could have used to find the probability in part b. Use this method to find the probability the chemical reacts in less than 40 of the processes. 2 Problem 4 (5P) The life length of a certain component follows an exponential distribution with mean 8 years. What is the probability a component lasts more than five years? Problem 5 (5P) IF X is a random variable following a chi-squared distribution with standard deviation 2, what is the probability that X takes at most the value 0.575? 5 Problem 6 (5p) Rate data often follow a lognormal distribution. Average power usage (dB per hour) for a particular company is studied and is known to have a lognormal distribution with parameters μ=4 and σ=2. What is the probability that the company uses more than 270 dB during any particular hour? Problem 7 (5p) Through thorough experimentation, you have knowledge that machine B3 averagely creates 4 defective products every 1 month. What is the probability that in any 3 consecutive months exactly five cigarette lighters are defective? What probability distribution do you use? What is the average rate? 6 Table A.3. The standard normal. Zz | 0.00 0.04 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 04 0.5398 0.5438 0.5478 Oss17 0.5557 0.5596 0.5636 0.5675 o5714 0.5753 02 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 03 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 04 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 06772 0.6808 0.6844 0.6879 O58 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 O06 0.7257 0.7291 0.7324 0.7357 0.7369 0.7422 0.7454 0.7486 0.7517 0.7549 7 0.7580 0.7611 0.7642 O.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 08 0.7881 0.7910 0.7939 0.7967 0.7995, 0.8023 0.8051 0.8078 0.8106 0.8133 O89 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 08315 0.8340 0.8365 0.8389 41.0 0.8413 0.6433 0.8461 0.8485, 0.8508 0.85341 0.8554 0.8577 0.8599 0.8621 14 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 12 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 43 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 09177 14 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 15 0.9332 0.9345, 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9447 1.6 0.9452 0.9463 0.9474 0.9484 0.9495, 0.9505, 0.9515 0.9525 0.9535 0.9545 17 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.6 0.9641 0.9649 0.9656 0.9664 0.9671 0.9676 0.9686 0.9693 0.9699 0.9706 19 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 24 0.9821 0.9826 0.9630 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 22 0.9861 0.95864 0.9668 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 23 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 24 0.9918 0.9920 0.9922 0.9925, 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 25 0.9938 o.9940 0.9941 0.9943, 0.9945, 0.9946 0.9948 0.9949 0.9951 0.9952 26 0.9953 0.9955, 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 27 0.9965 0.9966 0.9967 0.9963 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 28 0.9974 0.9975 0.9976 O9977 0.9977 0.9978 039979 0.9979 0.9980 0.9981 2a 0.9981 0.9982 0.9982 0.9963 0.9964 0.9964 0.9985 0.9985 0.9986 0.9986 30 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 34 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 32 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995, 0.9995, 0.9995, 33 0.9995 0.9995 0.9995, 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 34 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998