At a sobriety checkpoint,the police screened 676 drivers and 6 were arrested for impaired driving.The 92% confidence interval for the true proportion of drivers who were impaired at that time would be _____.
A)[0.000,0.027]
B)[0.003,0.015]
C)[0.902,0.938]
D)[0.000,0.076]
E)[0.006,0.030]

Question

Quizplus · Accepted Answer

To find the confidence interval, we can use the formula:
CI = p̂ ± z*sqrt((p̂(1-p̂))/n)
where p̂ is the sample proportion, z is the z-score for the chosen confidence level, and n is the sample size.
In this case, p̂ = 6/676 = 0.0089 and n = 676. For a 92% confidence level, the corresponding z-score is 1.75 (found using a z-table or calculator). 
Plugging in these values, we get:
CI = 0.0089 ± 1.75*sqrt((0.0089*(1-0.0089))/676)
CI = [0.003, 0.015]
Therefore, the best choice is B.

At a Sobriety Checkpoint,the Police Screened 676 Drivers and 6