The Resources Conservation and Recovery Act mandates the tracking and disposal o

Question

The Resources Conservation and Recovery Act mandates the tracking and disposal of Hazardous waste produces at US facilities. Professional Geographer reported the hazardous-waste generation and disposal characteristics of 25 facilities. Only 6 of these facilities treated hazardous waste on site. If 7 facilities selected at random from these 25 facilities,

a. What is the probability that none of the seven facilities will treat hazardous waste on site?

b. What is the standard deviation of the number of chosen facilities that treat hazardous waste on site?

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
probability of hazardous waste on site = 6/25 = 0.24
a.
P( X = 0 ) = ( 7 0 ) * ( 0.24^0) * ( 1 - 0.24 )^7
= 0.1465
b.
Mean ( np ) =25 * 0.24 = 6
Standard Deviation ( npq )= 25*0.24*0.76 = 2.1354

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