A Vendor Offers Various T-Shirts for Sale on an Internet

question 24

Essay

A vendor offers various t-shirts for sale on an Internet commerce site.Some of his t-shirts sell quite well, others have yet to find an interested customer.The summary $$\begin{array} { | l | c | } \hline \bar { x } & 23 \\\hline \text { Median } & 15 \\\hline \text { Min } & 0 \\\hline \text { Q1 } & 3 \\\hline \text { Q3 } & 21 \\\hline \text { Max } & 82 \\\hline \text { sd } & 7.84 \\\hline\end{array}$$
statistics are listed on right, based on the number of sales
per month for each of 80 different t-shirt designs.
A.What is the shape of this distribution? Explain how you know.
B.If the vendor spends $2 per t-shirt in shipping costs, what is his average monthly costs
per t-shirt sold? What is the standard deviation of this cost? Show work.
c.As time passes, the vendor has simplified his profit calculation.He estimates that he has
monthly flat costs of $35, with a gain of $3.50 per t-shirt sold.What is the median of his
profit? The IQR?
d.What are the mean and standard deviation of his profit?
e.What is more appropriate in this case: using mean and standard deviation, or using
median and IQR?

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Definitions:

Fixed Costs

Costs that do not change with the level of production or sales within a short period, such as rent, salaries, and insurance.

Gross Margin Percentage

A profitability metric expressed as a percentage, calculated by subtracting the cost of goods sold from sales revenue and dividing the result by sales revenue.

Net Profit Margin

The percentage of revenue remaining after all operating expenses, interest, taxes, and preferred stock dividends have been deducted from a company's total revenue.

Return on Assets

A measure of a company's profitability relative to its total assets, indicating how efficiently a company uses its assets to generate earnings.