Alyssa and Gabriel play the following game. Alyssa rolls a die. If she rolls a 1, 2, or 3, Gabriel gives Alyssa $3. If Alyssa rolls a 4 or 5, Gabriel gives Alyssa $2. However, if Alyssa rolls a 6, she gives Gabriel $14. a) Determine Alyssa's expectation.
b) Determine Gabriel's expectation.

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. consider the data set 14, 6, 8, 15, 15. (a) use the defining formula, the computation formula, or a calculator to compute s. (round your answer to one decimal place.) s = 4.28 (b) multiply each data value by 3 to obtain the new data set 42, 18, 24, 45, 45. compute s. (round your answer to one decimal place.) s = 12.83 (c) compare the results of parts (a) and (b). in general, how does the standard deviation change if each data value is multiplied by a constant c? multiplying each data value by the same constant c results in the standard deviation remaining the same. multiplying each data value by the same constant c results in the standard deviation being |c| times as large. multiplying each data value by the same constant c results in the standard deviation increasing by c units. multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. (d) you recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.8 miles. your friend wants to know the standard deviation in kilometers. do you need to redo all the calculations? yes no given 1 mile ≠1.6 kilometers, what is the standard deviation in kilometers? (enter your answer to two decimal places.)