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pashok25 [27]
3 years ago
14

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of peopl

e who appear on the list that are actually caught. Step 2 of 2 : Suppose a sample of 517 suspected criminals is drawn. Of these people, 211 were captured. Using the data, construct the 98% 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.
Mathematics
1 answer:
koban [17]3 years ago
7 0

Answer:

<em>98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list</em>

(0.3583 , 0.4579)

Step-by-step explanation:

<u>Explanation</u>:-

<em>Given sample size 'n' = 517</em>

Given data Suppose a sample of 517 suspected criminals is drawn. Of these people, 211 were captured.

'x' =211

<em>The sample proportion</em>

                                   p^{-}  = \frac{x}{n} = \frac{211}{517} =0.4081

                                  q^{-} = 1-p^{-} = 1- 0.4081 = 0.5919

<em>98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list</em>

(p^{-}  - Z_{\frac{\alpha }{2}  } \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} + Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} }{n} } )

(0.4081  - 2.326   \sqrt{\frac{0.4081 (0.5919 )}{517} } , 0.4081+ 2.326\sqrt{\frac{0.4081(0.5919 }{517} } )

(0.4081-0.0498 , 0.4081 +0.0498)

(0.3583 , 0.4579)

<u><em>Conclusion</em></u>:-

<em>98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list</em>

(0.3583 , 0.4579)

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