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...

See similar textbooks

Similar questions

The heights of two year old females is approximately normally distributed with a mean of 33.7 inches and a standard deviation of 4.2 inches. If 750 females that are two years of age are randomly chosen then how many would we expect to be shorter than 24.5 inches or taller than 46.1 inches. Give your answer to two decimal places and do not give units.
Consider again the birth weights of newborn babies, where the mean weight is 3290 grams and the standard deviation is 520 grams. Find the weight, in grams, that would separate the smallest 4% of weights of newborns from the rest.
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 3000 grams and a standard deviation of 600 grams while babies born after gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 440 grams. If a 32 week gestation period baby weighs 3225 grams and a 41 week gestation and 41 week gestation period baby weighs 3425 grams find the corresponding z scores which baby weigh more relative to the gestation period
In a survey, the mean weight of 1005 rats was calculated to be 132 gr. The standard deviation of the observation was found to be s=3 gr. Determine at least how many of the surveyed rats have a weight between 124.5 and 139.5 gr.
"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for two types of treated fabrics: Permafresh 15 12 16 13 11 14 10 Hylite 16 20 18 15 19 A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. Give a 90% confidence interval for the difference in mean wrinkle recovery angle: [three decimal accuracy] [three decimal accuracy]
A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is.x₁ = 1.15 and S₁ = 0.11, while for the 20-mil film, the data yield 2 = 1.06 and s2 = 0.09. Note that an increase in film speed would lower the value of the observation in microjoules per square inch. Do the data support the claim that reducing the film thickness increases the mean speed of the film? Use a = 0.10 and assume that the two population variances are equal and the underlying population of film speed is normally distributed. The appropriate decision for the test is to reject the null hypothesis True False
A professor gives a test to her calculus students. The scores are approximately normally distributed with mean 75 points and standard deviation 9 points. The professor decides to give As to approximately 10% of the students but not less than 10%. Find the cutoff score for an A.
Based on daily measurements, Brenda's weight has a mean of 200 pounds with a standard deviation of 16 pounds, while Karen’s weight has a mean of 125 pounds with a standard deviation of 15 pounds. Who has the smaller coefficient of variation?
The scores on a test are normally distributed with a mean of 150 and a standard deviation of 30. Find the score that is 2 1/2 standard deviations above the mean.
In a survey, the mean weight of 1032 rats was calculated to be 132 gr. The standard deviation of the observation was found to be s=3 gr. Determine at least how many of the surveyed rats have a weight between 124.5 and 139.5 gr.
A California lake has been stocked with rainbow trout. These trout have an average length of 24 inches, with a standard deviation of 3 inches. Someone goes fishing and catches a trout that is 26.25 inches long. Express the length of this trout in standard units, relative to all the trout that were used to stock the lake. Choose the answer below that is closest.
"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for two types of treated fabrics: Permafresh 12 13 15 11 10 16 14 Hylite 14 19 20 16 A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. Give a 98% confidence interval for the difference in mean wrinkle recovery angle: [three decimal accuracy] [three decimal accuracy]