The mean of the sample of 65 customer satisfaction ratings in Table L.7 is = 42.95. If we let μ denote the mean of all possible customer satisfaction ratings for the XYZ Box video game system, and assume that σ equals 2.64:
a. Calculate 95 percent and 99 percent confidence intervals for .
b. Using the 95 percent confidence interval, can we be 95 percent confident that  is at least 42 (recall that a very satisfied customer gives a rating of at least 42)? Explain.
c. Using the 99 percent confidence interval, can we be 99 percent confident that  is at least 42? Explain.
d. Based on your answers to parts b and c, how convinced are you that the mean satisfaction rating is at least 42?