Cassandra's Cogs advertises on its website that 90% of customer orders are received within three working days. They performed an audit from a random sample of 100 of the 2,500 orders that month and it shows 85 orders were received on time. Part A: Can we use a normal approximation? Explain. (5 points) Part B: If Cassandra's Cogs customers receive 90% of their orders within three working days, what is the probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less? (5 points) (10 points)

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above