Questions: The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete parts (a) through (e). Weapon Probability Handgun 0.473 Rifle 0.022 Shotgun 0.032 Unknown firearm 0.148 Knives 0.134 Hands, fists, etc. 0.053 Other 0.138 (d) What is the probability that a randomly selected murder resulted from a weapon other than a gun? P (weapon other than a gun) = 0.325 (Type a decimal rounded to three decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. A. If 1000 murders were randomly selected, exactly of them would have resulted from a weapon other than a gun. B. If 1000 murders were randomly selected, we would expect about of them to be have resulted from a weapon other than a gun.

The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete parts (a) through (e). Weapon Probability Handgun 0.473 Rifle 0.022 Shotgun 0.032 Unknown firearm 0.148 Knives 0.134 Hands, fists, etc. 0.053 Other 0.138 (d) What is the probability that a randomly selected murder resulted from a weapon other than a gun? P (weapon other than a gun) = 0.325 (Type a decimal rounded to three decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. A. If 1000 murders were randomly selected, exactly of them would have resulted from a weapon other than a gun. B. If 1000 murders were randomly selected, we would expect about of them to be have resulted from a weapon other than a gun.
Transcript text: The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete parts (a) through (e). \begin{tabular}{lr} Weapon & Probability \\ Handgun & 0.473 \\ \hline Rifle & 0.022 \\ \hline Shotgun & 0.032 \\ \hline Unknown firearm & 0.148 \\ \hline Knives & 0.134 \\ \hline Hands, fists, etc. & 0.053 \\ \hline Other & 0.138 \\ \hline \end{tabular} (d) What is the probability that a randomly selected murder resulted from a weapon other than a gun? $P$ (weapon other than a gun) $=0.325$ (Type a decimal rounded to three decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. A. If 1000 murders were randomly selected, exactly $\square$ of them would have resulted from a weapon other than a gun. B. If 1000 murders were randomly selected, we would expect about $\square$ of them to be have resulted from a weapon other than a gun.
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Solution

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Solution Steps

To solve this problem, we need to interpret the given probability and use it to make a prediction about the number of murders resulting from a weapon other than a gun out of 1000 randomly selected murders. The probability given is 0.325, which means 32.5% of the murders are expected to be from a weapon other than a gun. We will multiply this probability by 1000 to find the expected number of such murders.

Step 1: Identify the Given Probability

The given probability that a randomly selected murder resulted from a weapon other than a gun is \( P(\text{weapon other than a gun}) = 0.325 \).

Step 2: Determine the Total Number of Murders

We are asked to consider 1000 randomly selected murders. Thus, the total number of murders is \( 1000 \).

Step 3: Calculate the Expected Number of Murders

To find the expected number of murders resulting from a weapon other than a gun, we multiply the given probability by the total number of murders: \[ \text{Expected number of murders} = P(\text{weapon other than a gun}) \times \text{total number of murders} \] Substituting the values: \[ \text{Expected number of murders} = 0.325 \times 1000 = 325 \]

Step 4: Interpret the Probability

The interpretation of the probability is that if 1000 murders were randomly selected, we would expect about 325 of them to have resulted from a weapon other than a gun.

Final Answer

The answer is B: \[ \boxed{\text{If 1000 murders were randomly selected, we would expect about 325 of them to have resulted from a weapon other than a gun.}} \]

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