Laila is visiting the grounds of an ancient burial site in the shape of a pyramid and is hoping to find old buried artifacts and sell them to a museum. Historians have told her that there is only 1 undiscovered artifact per side of the pyramid. She plans to look on all 4 sides of the pyramid and assumes that on each side there is a 50, percent chance of her finding that side’s artifact independent of the other sides. The table below shows the resale value depending on how many artifacts she finds. What is the expected value of the resale value of the artifacts Laila finds?

Artifacts found 0 1 2 3 4

Resale value $0 $100 $250 $500 $1000

$306.25 (Khan)

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