According to a report 70.4% of murders are committed with a firearm. (a) If 200

Question

According to a report 70.4% of murders are committed with a firearm. (a) If 200 murders are randomly selected, how many would we expect to be committed with a firearm? (b) Would it be unusual to observe 158 murders by firearm in a random sample of 200 murders? Why? (a) We would expect to be committed with a firearm. (b) Choose the correct answer below. A. No, because 158 is greater than mu + 2sigma. B. No, because 158 is less than mu + 2sigma. C. Yes, because 158 is between mu - 2sigma and mu + 2sigma D. No, because 158 is between mu - 2sigma and mu + 2sigma. E. Yes, because 158 is greater than mu + 2sigma.

Explanation / Answer

p = 0.704, n = 200

Expected number of murders committed with firearm =n*p= 0.704*200 =140.8

Standard deviation = sqrt(n*p*(1-p)) = sqrt(200*0.704*(1-0.704)) = 6.455

mu + 2*sigma = 140.8 +2*6.455 = 153.71

=> 158 > mu + 2 sigma

Answer is-

Yes, because 158 is greater than mu+2*sigma

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