A company wants to evaluate their customer service's success and increase their salaries if they are successful. For this purpose they call their customers, and ask them to grade the customer service with a value from 1 to 10. The company would call the customer service successful if they get an average grade that is significantly higher than 7 from the customers. 17 customer replied the calls and the mean is 7.8. The standard deviation of any customer's response is 1.4. Assume the population is normally distributed where the standard deviation of any customer's response is 1.4 and each customer answered the question independently.

a) With 95% confidence, can the customer service be regarded as successful? Please state null and alternate hypotheses (H0 and HA).

b) What if one customer who gave 10 mistakenly gives 1? Can the customer service still be regarded as successful with 95% confidence?

c) For part b, what if there were 45 customers in the survey? Does the mistake still affect the customer service's success with 95% confidence? Briefly explain the results.

d) What if the threshold for success is set to 8 for 95% confidence. Briefly explain why we don't need to make any calculations to evaluate success in this case.

NOTE: For simplicity, assume that the standard deviation does not change in parts b and c.