A department store is implementing a loyalty card. Customers will earn "points" based on the dollar value of their purchases. The store will offer a signing incentive of 135 points every month and 0.26 points for every dollar the customer spends using their loyalty card. The following is the amount spent by a customer during the first 6-months with their loyalty card.
101.48 136.73 120.78 99.26 118.08 96.68
(a) The mean amount spent by the customer is $ and the standard devation of the amounts spent by the customer is $ .
(b) The mean number of loyalty points earned by the customer is and the standard deviation of the loyalty points earned is
(Hint: You don't need to convert every observation, you can just use your results from part (a)).
(c) Data was then gathered for a seventh month and it was found the customer spent $112.17. The mean amount spent by the customer over the 7-month period is $ .
(d) What would happen to the standard deviation of the amounts spend by the customer when this seventh observation is included?