Smith is a weld inspector at a shipyard. he knows from keeping track of good and substandard welds that for the afternoon? shift, 5% of all welds done will be substandard. if smith checks 300 of the 7500 welds completed that? shift, would it be unusual for smith to find 30 or more substandard? welds?

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11-08-2017
Mathematics

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Smith is a weld inspector at a shipyard. he knows from keeping track of good and substandard welds that for the afternoon? shift, 5% of all welds done will be substandard. if smith checks 300 of the 7500 welds completed that? shift, would it be unusual for smith to find 30 or more substandard? welds?

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barnuts barnuts · Answer 1 · 2017-08-23T16:21:42+02:00

The probability of finding a substandard weld is: p = 5% = 0.05
We are given that the sample size: n = 300
Using the Poisson Distribution , the average number of welds (m) is:

m = n*p =

m = 300 * 0.05
m =15

The standard deviation of welds (s) is calculated by:

s = sqrt (m)

s = sqrt (15)

s = 3.873

Assuming normal distribution, the z value corresponding to 30 sub standards is:
z =( X - Mean) / standard deviation
z =(30 - 15) / 3.873
z = 15 / 3.873
z = 3.87

The z value based on the standard normal curves has a maximum value of 3.49. Beyond that z value of 3.49 would mean exceeding 100%. Therefore z = 3.87 is not normal and definitely it is unusual to find 30 or more substandard.