Question 823139
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Hi,
"7% of al switches produced are defective. if 200 switches are selected at random, 
what us the probability that more than 20 will be defective?" 
<u>BINOMIAL Distribution</u> P(x) = nCx* {{{p^x*q^(n-x)}}} 
where p and q are the probabilities of success and failure respectively. 
In this case p = .07 & q = .93 & n = 200   nCx = {{{n!/(x!(n-x)!)}}}
 P(20) =(200C20)(.07)^20(.93)^180   Or binompdf(200, .07, 20)on calculator
Recommend using Your TI calculator for <u>cumulative probabilities</u>
and/or stattrek.com as an excellent reference.  
 P(x>20) = 1 - P(x &#8804; 20)  = 1 - binomcdf(200, .07, 20) on a Ti calculator
Without a Calculator: 1 - [ P(0) + P(1) + P(2) .... + P(20)]
Tedious, but can be done.
Again: stattrek.com is an excellent reference (also has calculators)