Problem

A car salesman sells cars with prices ranging from $\$ 5,000$ to $\$ 45,000$. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.
The salesman has observed that many students are looking for cars that cost less than $\$ 5,000$. If he decides to also deal in cars that cost less than $\$ 5,000$ and projects selling 200 of them over the next 10 years, how will the distribution be affected?
A. The mean will shift to the right.
B. The mean and the median will be the same.
C. The median will shift to the right.
D. The mean will shift to the left.
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Answer

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Answer

\(\boxed{\text{D. The mean will shift to the left.}}\)

Steps

Step 1 :The question is asking how the distribution of car prices will be affected if the salesman starts selling cars that cost less than $5,000. The salesman projects selling 200 of these cheaper cars over the next 10 years.

Step 2 :The mean of a distribution is the average value, calculated by summing all the values and dividing by the number of values. If the salesman starts selling cheaper cars, this will add a large number of lower values to the distribution, which will pull the mean down, or shift it to the left.

Step 3 :The median of a distribution is the middle value when all the values are arranged in ascending order. If the salesman starts selling cheaper cars, this will add a large number of lower values to the distribution, but it will not necessarily change the middle value, or the median.

Step 4 :Therefore, the correct answer is D. The mean will shift to the left.

Step 5 :\(\boxed{\text{D. The mean will shift to the left.}}\)

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