Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. a. What is the population mean of all possible sample proportions? b. What is the standard error of all possible sample proportions? c. What proportion of the samples are likely to have between 35% and 40% who take advantage of online customer service?

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**Online Customer Service and Sample Proportions: A Statistical Analysis**

**Context:**
Online customer service plays a crucial role in the success of online retailing. A marketing survey reveals that 37.5% of online customers utilize online customer service. For the purposes of analysis, random samples consisting of 200 customers are selected.

**Statistical Questions:**

a. **Population Mean of Sample Proportions:**
   - What is the population mean of all possible sample proportions?

b. **Standard Error of Sample Proportions:**
   - What is the standard error of all possible sample proportions?

c. **Proportion of Samples Between 35% and 40%:**
   - What proportion of the samples are likely to have between 35% and 40% who take advantage of online customer service?

d. **Percentage of Samples Less Than 37.5%:**
   - What percentage of the samples are likely to have less than 37.5% who take advantage of online customer service?
Transcribed Image Text:**Online Customer Service and Sample Proportions: A Statistical Analysis** **Context:** Online customer service plays a crucial role in the success of online retailing. A marketing survey reveals that 37.5% of online customers utilize online customer service. For the purposes of analysis, random samples consisting of 200 customers are selected. **Statistical Questions:** a. **Population Mean of Sample Proportions:** - What is the population mean of all possible sample proportions? b. **Standard Error of Sample Proportions:** - What is the standard error of all possible sample proportions? c. **Proportion of Samples Between 35% and 40%:** - What proportion of the samples are likely to have between 35% and 40% who take advantage of online customer service? d. **Percentage of Samples Less Than 37.5%:** - What percentage of the samples are likely to have less than 37.5% who take advantage of online customer service?
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