Question

According to a​ report, 78.5 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 335 murders by firearm in a random sample of 400 ​murders? Why?

Answer 1

(a)

n = 400

p = 0.785

q = 1 - p = 0.215

So,

= E(X) = Expected number of murders committed with a firearm = np = 400 X 0.785 = 314

So,

Answer is:

314

(b)

= np = 400 X 0.785 = 314

X = 335

Z = (335 - 314)/8.2164

= 2.5559

Since Z value corresponding to 335 murders by firearm is greater than 2, we conclude:

It would be unusual to observe 335 murders by firearm in a random sample of 400 murders.