SOLUTION: 7. Among companies doing highway or bridge construction, 80% test employees for substance abuse (based on data from the Construction Financial Management Association) A study inv

Question 507367: 7. Among companies doing highway or bridge construction, 80% test employees for substance abuse (based on data from the Construction Financial Management Association) A study involves the random selection of 12 such companies.
(a) Find the probability that exactly 7 of the 12 companies test for substance abuse.
(b) Find the probability that at least half of the companies test for substance abuse.
(c) For such group of 12 companies, find the mean and standard deviation for the number (among 12) that test for substance abuse.
(d) Using the results from part (c) and the range rule of thumb, indentify the range of usual value.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Among companies doing highway or bridge construction, 80% test employees for substance abuse (based on data from the Construction Financial Management
Association)
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A study involves the random selection of 12 such companies.
Binomial Problem with n = 12 and p = 0.8

(a) Find the probability that exactly 7 of the 12 companies test for substance abuse.
P(x = 7) = 12C7(0.8)^7*(0.2)^5 = 0.0532
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(b) Find the probability that at least half of the companies test for substance abuse.
P(7<= x <=12) = 1 - P(0<= x <=6) 1 - binomcdf(12,0.8,6) = 0.9806
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(c) For a group of 12 companies, find the mean and standard deviation for the number (among 12) that test for substance abuse.
mean = np = 12*0.8 = 7.2
std = sqrt(npq) = sqrt(7.2*0.2) = 1.2
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(d) Using the results from part (c) and the range rule of thumb, indentify the range of usual value.
If the "range of usual values" is 6*std, you get 6*1.2 = 7.2
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Cheers,
Stan H.
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