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A time-and-motion study measures the time required for an assembly-line worker to perform a repetitive task. The data show that the time required to bring a part from a bin to its position on an automobile chassis varies from car to car according to a Normal distribution with mean 11 seconds and standard deviation 2 seconds. The time required to attach the part to the chassis follows a Normal distribution with mean 20 seconds and standard deviation 4 seconds. The study finds that the times required for the two steps are independent. A part that takes a long time to position, for example, does not take more or less time to attach than other parts. Management's goal is for the entire process to take less than 30 seconds. Find the probability that this goal will be met for a randomly selected part.



Answer :

The amount of time required for an assembly line worker to complete a repetitive task is measured using a time and motion study.

According to the data, the average time it takes to move apart from the bin to its place on a car's chassis is 11 seconds, while the standard deviation is 2 seconds.

If XX and YY are independent, the property mean and variance are as follows: X 1 = 11; sigma_X_1 = 2, X 1 = 2, mu_X_2 = 20, X 2 = 20, sigma_X_2 = 4, and X 2 = 4.

aX+bY = a X + b Y; sigma_aX+bY = a X + b Y; aX+bY 2 = a 2 X 2 + b 2 Y 2; and finally, we have the following results:

X 1 + X 2 = X 1 + X 2 = 11+20=31 sigma_X_1+X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_1+

The value reduced by the mean and divided by the standard deviation is the z-score:

z=\dfrac{x-\mu} {\sigma} =\dfrac{30-4.4721} \approx - 0.22

z=σx−μ =4.472130−31

≈−0.22

Decide the relating esteem utilizing table A:

P (X_1+X_2 30) = P(Z-0.22) = 0.4129 P (X 1 30) = P(Z-0.22) = 0.4129

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