Customers are considered very satisfied with the XYZ Box video game system if the mean of the population of all satisfaction ratings is higher than 50. Assume that the standard deviation of the population of all satisfaction ratings is 4.64.
a. If the population mean of all satisfaction ratings is 50, what is the probability of observing a random sample of 80 satisfaction ratings with a mean greater than or equal to 51.45?
b. We have actually observed a random sample of 80 satisfaction ratings with a mean of 51.45. What do you conclude about whether customers are very satisfied with the XYZ Box video game system?