Suppose it is desired to establish the relationship between nominal dimensions o

Question

Suppose it is desired to establish the relationship between nominal dimensions of extension and sockets on hand tools in a situation similar to example presented in the lecture but involving different size. Assume that a study of consumer requirements indicated a desirable minimum clearance of 0.005 inch and a maximum clearance of 0.018 inch. Assume that a study of past production showed an average dimension of extension of 0.7510 with a standard deviation of 0.0015 and an average dimension of sockets of 0.7650 with a standard deviation of 0.0010. Both distributions are statistically controlled and approximately normal. What is the current average clearance? What is the standard deviation of the clearance? What is the probability that the randomly assembled pair will have smaller clearance than the desired minimum? What is the probability that the randomly assembled pair will have larger clearance than the desired maximum?

Explanation / Answer

Let's denote the socket size by X and extension size by Y

So, clearnce size, Z = X-Y

Given:

Mean socket size, X' = 0.7650, SX = 0.0010

Y' = 0.7510, SY = 0.0015

So, for clearance:

Z' = X'-Y' = 0.7650-0.7510 = 0.014

SZ = (SX2 + SY2)0.5 = 0.0018

P(Z < 0.005) is calculated as:

First calculate z-score: z = (0.005-0.015)/0.0018 = -5.55

From the cumulative z-table, the required probability is: p = 1.432*10-8

P(Z > 0.018) is calculated as:

First calculate z-score: z = (0.018-0.015)/0.0018 = 1.66

From the cumulative z-table, the required probability is: p = 0.049

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