The probability distribution of the fender thickness of car X, is a continuous random variable and...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The probability distribution of the fender thickness of car X, is a continuous random variable and can be approximated by Normal distribution with the probability density function as follows: 1 1 t f(t) = :exp (- 2 (3) Where t is the fender thickness, is the mean value, and o is the standard deviation of the distribution. The target value of the thickness, t, is 170mm. a) A new production line produces fender thickness with the mean value, , same as the target value and with the standard deviation o equivalent to 0.2mm. We know that the fender thickness has a specification interval of +- 0.4mm. Calculate the upper specification limit (USL) and the lower specification limit (LSL), respectively. Then calculate the fraction (percentage) of products that must be discarded. (z): Standard Normal CDF 2 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 01254 .0 5000 4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 .4602 .4562 .4522 .4483 4443 4404 .4364 4325 4286 .4247 .2 4207 .4168 .4129 .4090 .4052 4013 .3974 .3936 .3897 .3859 .3 .3821 .3783 3745 3707 .3669 .3632 .3594 .3557 .3520 .3483 .3446 .3409 .3372 .3336 3300 3264 .3228 .3192 .3156 .3121 I 56789 I 3085 .3050 .3015 2981 .2946 .2912 .2877 .2343 .2810 .2776 .2743 .2709 .2676 .2643 .2611 .2578 2546 2514 .2483 .2451 - .7 -.8 .2420 .2389 .2358 .2327 .2297 .2266 .2236 2206 .2177 .2148 .2119 2090 .2061 .2033 2005 .1977 .1949 .1922 .1894 .1867 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 -1.0 .1587 .1562 .1539 .1515 .1492 .1469 1446 .1423 .1401 .1379 -1.1 .1357 .1335 .1314 .1292 1271 .1251 .1230 .1210 .1190 .1170 -1.2 .1131 .1131 .1113 .1093 .1075 .1056 .1038 .1020 .1003 .09853 -1.3 .09680 .09510 .09342 .09176 .09012 .08851 .08691 .08534 .08379 .08226 -1.4 .08076 .07927 .07780 .07636 .07493 07353 07215 .07078 .06944 .06811 -1.5 .06681 .06552 .06426 .06301 .06178 .06057 .05938 .05821 .05705 .05592 -1.6 .05480 .05370 .05262 .05155 .05050 .04947 .04846 .04746 .04648 .04551 -1.7 .04457 -1.8 -1.9 .02807 .04363 .04272 .03593 .03515 .02872 .04182 .03438 .03362 .04093 .04006 .03288 .02743 .02680 .02619 .02559 .03920 .03216 .03144 .03074 .02500 .02442 .03836 .03754 .03673 .03005 .02938 .02385 .02330 -2.0 -2.1 -2.2 .01355 .02222 .02275 .01786 .01743 .01700 .01659 .01390 .02169 .02118 .02068 02018 01970 .01923 .01876 .01831 .01618 .01578 .01539 .01500 .01463 .01426 .01321 .01287 .01255 .01222 .01191 .01160 .01130. .01101 -2.3 .01072 .01044 .01017 .0 9903 .0-9642 .09387 .09137 .028894 .0 8656 .08424 -2.4 .0 8198 .07976 ,0*7760 .0-7549 .077344 07143 .06947 .06756 .0-6569 .06387 -2.5 .076210 .0-6037 .0 5868 .05703 .05543 .05386 05234 .05085 04940 .04799 -2.6 .04661 .04527 .04396 04269 04145 .04025 03907 .03793 .03681 .0*3573 -2.7 .03467 .03364 .0*3264 .03167 03072 .02980 .0 2890 .0-2803 .0-2718 .022635 -2.8 .02555 .0 2477 -2.9 .0*1866 .0*2401 .02327 .0 2256 .02186 .02118 .0-2052 .0 1988 .01926 .0F1807 0-1750 01695 .01641 01589 01538 .01489 .0*1441 .021395 The probability distribution of the fender thickness of car X, is a continuous random variable and can be approximated by Normal distribution with the probability density function as follows: 1 1 t f(t) = :exp (- 2 (3) Where t is the fender thickness, is the mean value, and o is the standard deviation of the distribution. The target value of the thickness, t, is 170mm. a) A new production line produces fender thickness with the mean value, , same as the target value and with the standard deviation o equivalent to 0.2mm. We know that the fender thickness has a specification interval of +- 0.4mm. Calculate the upper specification limit (USL) and the lower specification limit (LSL), respectively. Then calculate the fraction (percentage) of products that must be discarded. (z): Standard Normal CDF 2 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 01254 .0 5000 4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 .4602 .4562 .4522 .4483 4443 4404 .4364 4325 4286 .4247 .2 4207 .4168 .4129 .4090 .4052 4013 .3974 .3936 .3897 .3859 .3 .3821 .3783 3745 3707 .3669 .3632 .3594 .3557 .3520 .3483 .3446 .3409 .3372 .3336 3300 3264 .3228 .3192 .3156 .3121 I 56789 I 3085 .3050 .3015 2981 .2946 .2912 .2877 .2343 .2810 .2776 .2743 .2709 .2676 .2643 .2611 .2578 2546 2514 .2483 .2451 - .7 -.8 .2420 .2389 .2358 .2327 .2297 .2266 .2236 2206 .2177 .2148 .2119 2090 .2061 .2033 2005 .1977 .1949 .1922 .1894 .1867 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 -1.0 .1587 .1562 .1539 .1515 .1492 .1469 1446 .1423 .1401 .1379 -1.1 .1357 .1335 .1314 .1292 1271 .1251 .1230 .1210 .1190 .1170 -1.2 .1131 .1131 .1113 .1093 .1075 .1056 .1038 .1020 .1003 .09853 -1.3 .09680 .09510 .09342 .09176 .09012 .08851 .08691 .08534 .08379 .08226 -1.4 .08076 .07927 .07780 .07636 .07493 07353 07215 .07078 .06944 .06811 -1.5 .06681 .06552 .06426 .06301 .06178 .06057 .05938 .05821 .05705 .05592 -1.6 .05480 .05370 .05262 .05155 .05050 .04947 .04846 .04746 .04648 .04551 -1.7 .04457 -1.8 -1.9 .02807 .04363 .04272 .03593 .03515 .02872 .04182 .03438 .03362 .04093 .04006 .03288 .02743 .02680 .02619 .02559 .03920 .03216 .03144 .03074 .02500 .02442 .03836 .03754 .03673 .03005 .02938 .02385 .02330 -2.0 -2.1 -2.2 .01355 .02222 .02275 .01786 .01743 .01700 .01659 .01390 .02169 .02118 .02068 02018 01970 .01923 .01876 .01831 .01618 .01578 .01539 .01500 .01463 .01426 .01321 .01287 .01255 .01222 .01191 .01160 .01130. .01101 -2.3 .01072 .01044 .01017 .0 9903 .0-9642 .09387 .09137 .028894 .0 8656 .08424 -2.4 .0 8198 .07976 ,0*7760 .0-7549 .077344 07143 .06947 .06756 .0-6569 .06387 -2.5 .076210 .0-6037 .0 5868 .05703 .05543 .05386 05234 .05085 04940 .04799 -2.6 .04661 .04527 .04396 04269 04145 .04025 03907 .03793 .03681 .0*3573 -2.7 .03467 .03364 .0*3264 .03167 03072 .02980 .0 2890 .0-2803 .0-2718 .022635 -2.8 .02555 .0 2477 -2.9 .0*1866 .0*2401 .02327 .0 2256 .02186 .02118 .0-2052 .0 1988 .01926 .0F1807 0-1750 01695 .01641 01589 01538 .01489 .0*1441 .021395
Expert Answer:
Related Book For
Making Hard Decisions with decision tools
ISBN: 978-0538797573
3rd edition
Authors: Robert Clemen, Terence Reilly
Posted Date:
Students also viewed these mathematics questions
-
can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...
-
(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...
-
Which will undergo the greater rate of cooling: a red-hot poker in a warm oven or a red-hot poker in a cold room (or do both cool at the same rate)?
-
If Sue rents her vacation home to her nephew at fair rental value, will his use of the home be considered "personal use" for purposes of the vacation home deduction rules?
-
An armored car transports money between two locations and travels along one of three routes: \(A_{1}, B_{1}, C_{1}\). On one day, the route is randomly selected according to the probabilities...
-
Incubators are organizations that provide startups with shared operating space. They are sponsored by universities, city or county governments, or nonprofit organizations. Incubators also provide...
-
Rains Nickless Ltd. of Australia has two divisions that operate in Perth and Darwin. Selected data on the two divisions follow: Required: 1. Compute the return on investment (ROI) for each division....
-
Assume the export price of a Nissan car from Japan is Yen 3,000,000. The exchange rate is Yen 122.00/$. A forecast on inflation in the USA is 2% and 0% in Japan per annum. Assuming purchasing power...
-
8. Benin had a population of 7.2 million in 2012. If the population is expected to grow to 12.4 million by 2060, what is the growth rate? (10 points)
-
Consider these functions: (2) = 1 + 4 g(x)=9x - 12 What is the value of g(f(x))?
-
Shiigi Urban Diner is a charity supported by donations that provides free meals to the homeless. The diner's budget for May is to be based on 3,450 meals. The diner's director has provided the...
-
Spotted Cow Dairy Company manufactures three productswhole milk, skim milk, and creamin two production departments, Blending and Packing. The factory overhead for Spotted Cow Dairy is $299,700. The...
-
Why supply chain management has an important role for companies?
-
you just drove your car 300 miles and used 40 gallons of gas. You know that the gas tank on your car holds 16(1)/(2) gallons of gas. What is the most number of miles you can drive on one tank of gas?
-
Answer the following questions: 1. What is risk? 2. Explain how to mitigate or manage risk. 3. Explain Systematic Risk. 4. What is Illiquidity risk? 5. How can Diversification impact risk? 6. Explain...
-
You are a U.S. investor who purchased British securities for 2,000 one year ago when the British pound cost U.S. $1.50. What is your total return (based on U.S. dollars) if the value of the...
-
Two samples of ideal gas, sample 1 and sample 2, have the same thermal energy. Sample l has twice as many atoms as sample 2. What can we say about the temperatures of the two samples? A. T>T B. T = T...
-
Which of the following changes (there may be more than one) would increase the maximum theoretical efficiency of a heat engine? A. Increase T H B. Increase T c C. Decrease T H D. Decrease T c
-
Which of the following processes does not involve a change in entropy? A. An electric heater raises the temperature of a cup of water by 20C. B. A ball rolls up a ramp, decreasing in speed as it...
Study smarter with the SolutionInn App