"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, what is the probability that he will find more than 25 substandard welds?"
A) .4960
B) .5040
C) .0040
D) .9960
....I have no idea how to work this problem. Can someone please explain to me how to? PLEASE...
2 Answers

Probability of finding a substandard weld = p = 5% = 0.05
Sample size = n= 300
According to Poisson Distribution
the average number of welds= m = np = 300 0.05
=15
the stadard deviation of welds = Square root of m = sqrt of 15 = 3.873
By using Normal distribution, z value corresponding to 25 is to be calculated
z =( X  Mean) / standard deviation =(25  15) / 3.873 = 10 / 3.873 = 2.58
According to the Area under Stadard Normal Curve tables
Area right to z=2.58 is to be located
It comes to 0.0040 approximately
So the probability of finding more than 25 substandard welds = 0.0040
The answer to the question is (c)

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, what is the probability that he will
find less than 20 substandard welds?