CFA Practice Question
CFA Practice Question
On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production employees are to be selected at random for a special in-depth study on absenteeism. What is the probability of selecting 10 production employees at random on a hot summer day and finding that none of them are absent?
Explanation: This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by: n!(pr)[q(n-r)]/r!(n-r)!. Here, n = 10, r = 0,p = 0.05 and q = 0.95. Therefore we have 10!(0.050)(0.9510)/0!10! = 0.599.
User Contributed Comments 11
|G3cc0||you can also conceptualize this prob as P(not absent) = .95, so .95^10=.599|
|lwang014||I agree with G3cc0's method which is esaier|
|DAS11||I also used P(not absent)|
|itconcepts||hey, if you managed to select them, they cant be absent, right?|
|itconcepts||ok, on a serious note, G3ccO's method must be a coincidence? if you had 100 employees you can't select 96 and still find none absent - while .95^96 will still give you a probability of .0073 ?|
|itconcepts||ok again, maybe not - the official formula gives the same result trying it with 96....hmmn, the flaw here is the sample size?
|malawyer||@itconcepts: the number of workers is irrelevant in this case - it just asks of a sample size which is lower than the population-estimated absence|
|Photon||Thank you Analyst Notes|
|jjhigdon||The "short cut" method only works for all or none examples. If it were to ask for the probability of selecting 10 employees and finding 3 of them absent, you would need to apply the formula from the explanation. Further more it could ask for the probability that less than 3 or more than 7 of the 10 are absent, in which case you also need to know the proper formula...|
|jjhigdon||Which is much less confusingly stated as:
nCr x P^r x (1-P)^n-r
because you can quickly and easily use the calculator to solve nCr...
(10 2nd nCr 10) * (.05)^0 * (.95)^10 = .5987