Two devices are used to measure the length of beam. If the true length of the beam is L, the measurementerror made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L, and themeasurement error made by the other device, E, , is normally distributed with mean 0 and standarddeviation 0.004L. The two measurement errors are independent of each other. What is the probability thatthe average value of the two measurements, (E, + E,)/2, is within 0.5% of L?Note that this problem can be done using the attached table of the cdf of the standard normal random variable. z is the standard normal variable. The value of P for -z, equals 1 minus thevalue of P for +zp; for example, the P for -1.62 equals 1-.9474 = .0526..00.01.02.03.04.05.06.07.08.095359.5753.0.5000.5040.5080.5120.5160.5199.5239.5279.5319.5398.5438.5478.5517.5557.5596.56365675.5714.2.5793.58325871591059485987.6026.6064.6103.6141.3.6179.6217.6255.6293.6331.6368.6406.6443.6480.6517.4.6554.6591.6628.6664.6700.6736.6772.6808.6844.6879.56915.6950.7019.7054.7088.7123.7454.6985.7157.7190.7224.6.7257.7291.7324.7357.7389.7422.7486.7517.7549.7.7580.7611.7642.7673.7704.7734.7764.7794.7823.7852.8.7881.7910.7939.7967.7995.8023.8051.8078.8106.8133.9.8159.8186.8212.8238.8264.8289.8315.8340.8365.83891.0.8413.8438.8461.8485.8508.8531.8554.8577.8599.86211.1.8643.86658686.8708.8729.8749.8770.8790.8810.88301.28849.8869.8888.8907.8925.8944.8962.89808997.9015.9049.9115.9131.9147.92921.3.9032.9066.9082.9099.9162.91771.4.91929207.9222.9236.9251.9265.9279.9306.93191.5.9332.9345.9357.9370.9382.9394.9406.9418.9429.9441.9452.9554.9474.9484.9495.9505.9515.9525.9535.9625954596331.6.94631.7.9564.9573.9582.9591.9599.9608.96161.8.9641.9649.9656.9664.9671.9678.9686.9693.9699.97061.9.9713.9719.9726.9732.9738.9744.9750.9756.9761.97672.0.9772.9778.9783.9788.9793.9798.9803.9808.9812.98172.1.9821.9826.9830.9834.9838.9842.9846.9850.9854.98572.2.9861.9864.9868.9871.9875.9878.9881.9884.9887.98902.3.9893.9896.9898.9901.99049906.9909.9911.991399162.4.9918.9920.9922.9925.9927.9929.9931.9932.9934.99362.5.9938.9940.9941.9943.9945.9946.9948.9949.9951.9952.9957.9968.99772.6.9953.9955.9956.9959.9960.9961.9962.9963.99642.7.9965.9966.9967.9969.9970.9971.9972.9973.99742.8.9974.9975.9976.9977.9978.9979.9979.9980.99812.9.9981.9982.9982.9983.99849984.9985.9985.9986.99863.0.9987.9987.99879988.9988.99899989.99899990.99903.1.9990.9991.9991.9991.9992.9992.9992.9992.9993.99933.2.9993.9993.9994.9994.9994.9994.9994.9995.9995.99953.3.9995.9995.9995.9996.9996.9996.9996.9996.9996.99973.4.9997.9997.9997.9997.99979997.9997.9997.9997.9998

E1 is normally distributed with a mean μ1 0 and standard deviation of (σ1) 0.006L E2 is normally…

Two devices are used to measure the length of beam. If the true length of the beam is L, the measur error made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L. measurement error made by the other device, E, , is normally distributed with mean 0 and standar deviation 0.004L. The two measurement errors are independent of each other. What is the proba the average value of the two measurements, (E, + E,)/2, is within 0.5% of L? Note that this problem can be done using the attached table of the cdf of the standard normal randon

Two devices are used to measure the length of beam. If the true length of the beam is L, the measur error made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L. measurement error made by the other device, E, , is normally distributed with mean 0 and standar deviation 0.004L. The two measurement errors are independent of each other. What is the proba the average value of the two measurements, (E, + E,)/2, is within 0.5% of L? Note that this problem can be done using the attached table of the cdf of the standard normal randon

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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