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

"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?

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