SOLUTION: A recent survey shows that 60% of the factory workers willing to work overtime without extra pay as long as they are guaranteed job security and bonus at the end of the year. Fif

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Question 872851: A recent survey shows that 60% of the factory workers willing to work overtime
without extra pay as long as they are guaranteed job security and bonus at the
end of the year. Fifteen factory workers are randomly selected, find (Use binomial
formula):
(a) The mean and standard deviation of the number of workers who are willing to
work overtime without extra pay. (2 marks)
(b) The probability that at least 13 workers are willing to work overtime without
extra pay. (3 marks)
(c) The probability that 10 workers are unwilling to work overtime without extra
pay. (2 marks)
(d) Explain why a binomial distribution is suitable for computing probabilities of
the number of workers who are willing to work overtime without pay. (3 marks)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

p(willing to work overtime without pay) = .6,  n = 15

a) Mean = .6*15 = 9, sd = √9 = 3

b) P(x ≥ 13) =   1 - binomcdf(15, .6, 12) = .0271

c) P(x=10) = 15C10(.6)^10(.4)^4   0r  binompdf(15, .6, 10)= .1859

Single x-value

P+%28x%29=+highlight_green%28nCx%29%28p%5Ex%29%28q%29%5E%28n-x%29+ 

p and q are the probabilities of success and failure respectively. 

In this case p = .6 & q = .4

nCx+=+%28n%21%29%2Fx%21%28n+-+x%29%21%29