Suppose you are going to roll a die 60 times and record the proportion pˆ of times that an even number (2, 4, 6) is showing. (a) The sampling distribution should be centered about what value? What kind of estimator is pˆ? (b) If you roll the die 600 times, then pˆ should be very close to 1 . What is this phenomenon called?

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?