Question

A 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.

how would the shape of the distribution change if the salesman decides to also deal in cars priced under $5,000 and in cars $45,000 to $50,000 and projects sales of 200 cars in each category?

a. the distribution will exhibit symmetry.

b. the distribution will exhibit a positive skew.

c. the distribution will exhibit a negative skew.

d. the distribution will uniform throughout.

Answer 1

If the salesman decides to also deal in cars priced under $5,000 and in cars $45,000 to $50,000 and projects sales of 200 cars in each category, the shape of the distribution would exhibit a positive skew.

Step-by-step explanation:

If the salesman decides to also deal in cars priced under $5,000 and in cars $45,000 to $50,000 and projects sales of 200 cars in each category, the shape of the distribution would exhibit a positive skew (b).

An additional category of cars priced under $5,000 would introduce a cluster of low-priced cars, which would result in a longer tail on the left side of the histogram, causing a positive skew. Similarly, adding a category of cars priced $45,000 to $50,000 would introduce a cluster of high-priced cars, resulting in a longer tail on the right side of the histogram.

This change in the distribution shape is because the new categories have extreme values (very low or very high prices) that shift the overall distribution towards the right.

Answer 2

In the given histogram, the shape of the histogram shows that the shape of the distribution exhibits symmetry (i.e. the shorter bars are to the left and to the right while the longer bars are in the middle). Adding the sales of cars priced under $5,000 and cars priced $45,000 to $50,000 with projected sales of 200 cars for each category will result in adding bars of the same size as the shortest bar to both ends of the histogram. This will not affect the initial shape of the distribution in the histogram as the distribution will still exhibit symmetry. Therefore, the correct answer to the question is "the distribution will exhibit symmetry" (option a).