Question

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2 : Suppose a sample of 523 suspected criminals is drawn. Of these people, 141 were captured. Using the data, construct the 95% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.

Lower End Point_____________________

Upper End Point _____________________

Answer 1

Answer)

Given N = 523

P = 141/523

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 141

N*(1-p) = 412

As both are greater than 5, conditions are met and we can use standard normal z table to construct the interval

Critical value z for the 95% confidence level is 1.96

Margin of error (MOE) = Z*√P*(1-P)/√N

P = 141/523

N = 523

Z = 1.96

MOE = 0.03803161568

Lower limit = P-MOE = 0.23156685467 = 0.232

Upper limit = P+MOE = 0.30763008605 = 0.308