Question

according to a report, 70.5% of murders are committed with a firearm
(a) if 300 murders are randomly selected, how many would we expect to be committed with a firearm?
(b) would it be unusual to observe 221 murders by firearm in a random sample of 300 murders? why?
(a) we would expect □ to be committed with a firearm.

Explanation:

Step1: Calculate the expected number

The formula for the expected value \(E(X)\) of a binomial distribution is \(E(X)=n\times p\), where \(n = 300\) (sample size) and \(p=0.705\) (probability of a murder being committed with a firearm).

$$E(X)=300\times0.705$$

Step2: Perform the multiplication

$$300\times0.705 = 211.5$$

Answer:

\(211.5\)