To solve this problem, let's break it down step by step:
1. Calculate the total number of survey responses:
- Small: 11
- Medium: 37
- Large: 83
- Extra-large: 19
Sum these up to get the total number of responses:
[tex]\[
11 + 37 + 83 + 19 = 150
\][/tex]
2. Determine which T-shirt size received the most responses:
- Small: 11
- Medium: 37
- Large: 83
- Extra-large: 19
The size with the highest number of responses is "large," with 83 responses.
So, the company should focus on producing large T-shirts.
3. Calculate the combined percentage of medium and large T-shirts:
- Medium: 37
- Large: 83
Total medium and large responses:
[tex]\[
37 + 83 = 120
\][/tex]
Percentage of medium and large responses:
[tex]\[
\left( \frac{120}{150} \right) \times 100 \approx 80.0\%
\][/tex]
4. Calculate how many small T-shirts will likely be sold in a month out of 45,000 total T-shirts sold:
First, find the proportion of small T-shirt responses:
[tex]\[
\frac{11}{150}
\][/tex]
Then, multiply this proportion by the total number of T-shirts sold in a month:
[tex]\[
45000 \times \left( \frac{11}{150} \right) = 45000 \times \frac{11}{150} = 3300
\][/tex]
So, the company should focus on producing large T-shirts. Approximately 80.0% of T-shirts the company makes should be medium and large T-shirts to match the market preference. If the total number of T-shirts sold in a month is 45,000, then 3300 of these will likely be size small.
