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According to a report, 59.9% 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 198 murders by firearm in a random sample of 300 murders? Why?

(a) We would expect 179.7 to be committed with a firearm.

(b) Choose the correct answer below:

A. No, because 198 is greater than μ + 20.

B. No, because 198 is between μ - 20 and μ + 20.

C. No, because 198 is less than μ - 20.

D. Yes, because 198 is greater than μ + 20.

E. Yes, because 198 is between μ - 20 and μ + 20.

Answer :

(a) we would expect approximately 179.7 murders to be committed with a firearm in a sample of 300 murders.(b) observing 198 murders by firearm falls within this range and would not be considered unusual.

(a) To calculate the expected number of murders committed with a firearm, we multiply the proportion (59.9%) by the total number of murders (300): 0.599 * 300 = 179.7. Therefore, we would expect approximately 179.7 murders to be committed with a firearm in a sample of 300 murders.

(b) To assess whether observing 198 murders by firearm in a sample of 300 is unusual, we need to consider the expected range of values. If the observed value falls outside a specific range, it can be considered unusual. In this case, the correct answer is (B) No, because 198 is between μ-20 and μ+20. Since we expect around 179.7 murders by firearm based on the given proportion, we can consider the range of approximately μ-20 to μ+20 as the expected range. Therefore, observing 198 murders by firearm falls within this range and would not be considered unusual.

In conclusion, the expected number of murders committed with a firearm in a sample of 300 is approximately 179.7. Observing 198 murders by firearm in this sample would not be considered unusual since it falls within the expected range.

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