Question

According to a​ report, 72.2​% of murders are committed with a firearm. ​(a) If 400 murders are randomly​ selected, how many would we expect to be committed with a​ firearm? ​(b) Would it be unusual to observe 322 murders by firearm in a random sample of 400 ​murders? Why? ​(a) We would expect nothing to be committed with a firearm. ​(b) Choose the correct answer below. A. ​No, because 322 is less than mu minus 2 sigma. B. ​No, because 322 is greater than mu plus 2 sigma. C. No​, because 322 is between mu minus 2 sigma and mu plus 2 sigma . D. ​Yes, because 322 is between mu minus 2 sigma and mu plus 2 sigma. E. Yes​, because 322 is greater than mu plus 2 sigma .

Answer 1

The mean proportion here is given as: p = 0.722

The standard deviation here is computed as:

a) The expected number we would expected to be committed with a firearm is computed here as:

= 0.722*400 = 288.8

Therefore 288.8 is the expected number here.

b) We compute the range here as:

Now, 0.7668*400 = 306.72

As 306.72 < 322, therefore E. Yes​, because 322 is greater than mu plus 2 sigma is the correct answer here.