Question

According to a​ report, 79.2​% 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 173 murders by firearm in a random sample of 200 ​murders? Why?

Answer 1

Explanation:

Given that the proportion of murders with firearm is 79.2 %

Each murder is independent and there are two outcomes either with fire arm or without fire arm.

Hence X no of murders with fire arm is binomial with n = 200 and p = 0.792

q=1-0.792 = 0.208

a) Expected value of x = np

`= 200(0.792)\\= 15.80`

b) P(X=173) = 0.002289

Since probability is very low it can be concluded it would be unusual to observe 173 murders by firearm in a random sample of 200 ​murders