The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company's success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown in the following table:



Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer had a high level of satisfaction and used the company less than two times per month?
Question 12 options:









To find the probability that a customer had a high level of satisfaction **and** used the company less than two times per month, we need to calculate a joint probability based on the information provided. However, since you have not provided the actual table, I’ll guide you through the steps.

### Steps to Solve:

1. **Identify the total number of customers surveyed** – This will help us determine the denominator for our probability calculation (i.e., the total sample space).

2. **Look for the number of customers who had a high level of satisfaction** and used the company less than two times per month – This will help us find the joint event (both high satisfaction and less than two uses per month).

3. **Compute the probability** – The probability of both events occurring together (i.e., high satisfaction and less than two uses) is calculated by dividing the number of favorable outcomes by the total number of customers.

### Formula:
\[
P(\text{high satisfaction and less than 2 uses}) = \frac{\text{Number of customers with high satisfaction and less than 2 uses}}{\text{Total number of customers surveyed}}
\]

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### Next Steps:
Please provide the table or the numbers from the study so I can plug them into the formula and calculate the probability for you.

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Would you like to provide that data or ask about any other related questions? 

### Related questions:
1. How do you calculate joint probabilities in a frequency table?
2. What are some other examples of calculating probabilities using survey data?
3. How would the probability change if we looked for high satisfaction and 2 or more uses per month?
4. How can conditional probability be applied in customer satisfaction surveys?
5. What role does sample size play in calculating probabilities?

**Tip**: Understanding how to interpret joint probabilities will help you when working with contingency tables and analyzing real-world data!

The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company's success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown in the following table. Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer had a high level of satisfaction and used the company less than two times per month?

Determine the probability that a customer had high satisfaction and used the overnight shipping service less than two times per month. Learn to apply joint probability in real-world scenarios involving customer satisfaction surveys, with a step-by-step breakdown.

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