Statistics question-please explain? (10 points!)?

Question

Smith is a weld inspector at a shipyard. He has tracked the quality of welds and found that, during the afternoon shift, 5% of all welds completed are substandard. For this shift, a total of 7,500 welds were completed, and Smith checked 300 of them. What is the probability that he will find more than 25 substandard welds among the 300 he inspected? 
A) 0.4960
B) 0.5040
C) 0.0040
D) 0.9960  
I am unsure how to approach this problem. Could someone please explain the solution step-by-step? Thank you!

Anonymous · Accepted Answer

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)

Clare Beer · Answer

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?

Anonymous

Statistics question-please explain? (10 points!)?

2 Answers

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