ariation ach night you total the day's sales and the total volume of ice cream sold in your shop. You notice that when an employee named Ben works, the mean price of the ice cream sold is $$ \$ 2.20 $$ per pint ith a standard deviation of $$ \$ 0.10 $$. On nights when an employee named Jerry works, the mean price of the ice cream sold is $$ \$ 2.25 $$ per pint with a standard deviation of $$ \$ 0.35 $$. Which employee likely ceives more complaints that his servings are too small? Explain. A. The means are nearly equal. However, because Ben's standard deviation is smaller, he likely serves more small portions. B. Jerry likely serves more small portions because he has a smaller mean. C. The means are nearly equal. However, because Jerry's standard deviation is larger, he likely serves more small portions. D. Ben likely serves smaller portions because he has a smaller mean. h. Bert answer below.

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UpStudy AI · Accepted Answer

To determine which employee likely receives more complaints about small servings, we need to analyze the mean prices and standard deviations of the ice cream sold by Ben and Jerry.

### Known Conditions:
- **Ben:**
  - Mean price per pint: $$ \mu_B = 2.20 $$
  - Standard deviation: $$ \sigma_B = 0.10 $$

- **Jerry:**
  - Mean price per pint: $$ \mu_J = 2.25 $$
  - Standard deviation: $$ \sigma_J = 0.35 $$

### Analysis:
1. **Mean Price Comparison:**
   - Ben's mean price is $$ 2.20 $$ and Jerry's is $$ 2.25 $$. The means are close, but Jerry's mean is slightly higher.

2. **Standard Deviation Comparison:**
   - Ben has a smaller standard deviation ($$ 0.10 $$) compared to Jerry's ($$ 0.35 $$). A smaller standard deviation indicates that Ben's prices are more consistent and closer to the mean, while Jerry's prices vary more widely.

3. **Implications of Standard Deviation:**
   - A smaller standard deviation (Ben) suggests that the prices are clustered closely around the mean. This means that while Ben's mean price is lower, the variation in his prices is less, which could imply that he serves more consistent portions.
   - A larger standard deviation (Jerry) indicates that there is a wider range of prices, which could mean that he serves both larger and smaller portions, leading to more variability in customer satisfaction.

### Conclusion:
Given that Ben has a smaller standard deviation, it is likely that he serves more consistent portions, which could lead to fewer complaints about small servings. In contrast, Jerry's larger standard deviation suggests that he has a wider range of serving sizes, which could lead to more complaints about small servings.

### Answer:
**A. The means are nearly equal. However, because Ben's standard deviation is smaller, he likely serves more small portions.**

This option correctly identifies that Ben's smaller standard deviation indicates more consistency in serving sizes, which could lead to fewer complaints about small servings.
Ben likely serves more consistent portions, so he receives fewer complaints about small servings.

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