Question

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?

Answer 1

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.