Question

An independent third party found the cost of a basic car repair service for a local magazine. The mean cost is $217.00 with a standard deviation of $11.40. Which of the following repair costs would be considered an “unusual” cost?

Answer 1

Given

An independent third party found the cost of a basic car repair service for a local magazine.

The mean cost is $217.00 with a standard deviation of $11.40.

To find: The repair costs which would be considered an “unusual” cost.

Step-by-step explanation:

It is given that, the mean is 217.00, and the standard deviation is 11.40.

Consider, the distribution as a Normal distribution.

Then, the first range is defined as,

`\begin{gathered} First\text{ }range:mean\pm SD \\ \Rightarrow X_1=mean+SD \\ =217.00+11.40 \\ =228.4 \\ \Rightarrow X_2=mean-SD \\ =217.00-11.40 \\ =205.6 \end{gathered}`

And, the second range is defined as,

`\begin{gathered} Second\text{ }range:mean\pm2SD \\ \Rightarrow X_3=217.00+2(11.40) \\ =217.00+22.8 \\ =239.8 \\ \Rightarrow X_4=217.00-2(11.40) \\ =217.00-22.8 \\ =194.2 \end{gathered}`

Hence, the answer is option a) 192.53 since it does not belongs to the above ranges.