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Suppose you are going to roll a fair 6 sided die 10 times and record p- hat, the proportion of times that 1 or a 2 is showing. questions: 1) what is the standard deviation of the sampling distribution of p-hat? interpret this value. 2) describe the sampling distribution of p-hat. justify your answer.

Asmall internet mail-order company keeps track of the number of orders it fills per day for many years and determines that the distribution of the variable "orders filled per day" is right-skewed and has the following five-number summary: minimum = 20 q1 = 32 median = 46 q3 = 63 maximum = 80 suppose we take random samples of size 40 from this distribution and calculate the range for each of our samples. (i cant put in the graph, but its approximately normal with center between 56 and 57, with a range of 53 to 60). a) there are two dots on the graph at 53. explain what these values represent. b) is the sample range an unbiased estimator of the population? use the dotplot above to justify your answer.

How can firms use marginal analysis to determine the price of a product? a) profit maximization can occur when the marginal cost exceeds the marginal revenue. b) the total cost of production can determine the individual unit price of a product. c) marginal analysis can be used to determine at what price profit maximization occurs. d) firms can calculate the marginal cost of a product and set the price lower than the cost.