Respuesta :
Answer: The answer is 135 murders.
Step-by-step explanation: The report tells us that statistically 67.5% of murders are committed using a firearm. It follows therefore that in a sample of 200 randomly selected murders, one would expect that 67.5% of those would be by a firearm. [tex]\frac{67.5}{100}[/tex] * 200 = 135.
It would certainly be higher that the expected value based on previous data collected but it would not be unusual because one sample may have a higher than "normal" amount of murders by firearm. Statistics aren't going to be exact for every sample.
Using the binomial distribution, it is found that:
a) The expected value is of 135.
b) Unusual, as 153 is more than 2.5 standard deviations above the mean.
What is the binomial probability distribution?
It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem, the parameters are p = 0.675 and n = 200.
Item a:
E(X) = np = 200 x 0.675 = 135.
135 would be expected to be committed with a firearm.
Item b:
The standard deviation is given by:
[tex]\sqrt{V(X)} = \sqrt{200(0.675)(0.325)} = 6.624[/tex]
Then:
[tex]E(X) + 2.5\sqrt{V(X)} = 135 + 2.5(6.624) = 151.56 < 153[/tex]
Since 153 is more than 2.5 standard deviations above the mean, it would be unusual observe 153 murders by firearm in a random sample of 200 murders.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
