The Eagles Hotel wants to determine the average amount a neighborhood customer spends per month at the Eagles. The owner incredibly has an email list of all their customers that live within a 5-block radius (the neighborhood). An email questionnaire asking about their spending per month is decided upon, but the owner doesn't want to send this email to all of the 100,000 people on the list. The owner knows that 20% of the people emailed will actually respond and is unworried about the responders differing from the responders. Management wants to be 99% confident of their findings and wants the accuracy to be plus or minus $5. The owner believes the population variance for spending per person per month is about $400.

a) How many people should be emailed with the questionnaire in order to get the required number of responses?

Show your work. (This required number of responses is your sample size)

b) The survey carried out using the sample size decided on in part a) revealed that the sample's average spend was $40 and the estimated variance for the population was a surprising $900.

What can be said about your actual level of accuracy? Show your work.

c) By how many people did The Eagles over or under sample? Show your work.