6In 1992 the FAA conducted 86991 preemployement drug tests o

6)In 1992, the FAA conducted 86,991 pre-employement drug tests on job applicants who were to be engaged in safety and security -related jobs,and found that 1,143 were positive. Which of the following is closest to a 90% confidence interval for the true proportion ,p,of individuals with positive drug tests? A.(0.0025,0.0038) B.(0.0125,0.0138) C,(0,0225,0.0238) D.(0.0325,0.0338) E.(0.0425,0.0438)

show work pls

Solution

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=1143
Sample Size(n)=86991
Sample proportion = x/n =0.0131
Confidence Interval = [ 0.0131 ±Z a/2 ( Sqrt ( 0.0131*0.9869) /86991)]
= [ 0.0131 - 1.64* Sqrt(0) , 0.0131 + 1.64* Sqrt(0) ]
= [ 0.0125,0.0138]