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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 6, 4, 11, 12, 7. l5 usss (a) Use the defining formula, the computation formula, or a calculator to compute 5. (Round your answer to four decimal places.) 5 = 3.4 x (b) Multiply each data value by 2 to obtain the new data set 12, 8, 22,24, 14. Compute 5. (Round your answer to four decimal places) 5 = (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 increasing by c units. Multiplying each data value by the same constant 6 results in the standard deviation being |c| times smaller. Multiplying each data value by the same constant 5 results in the standard deviation remaining the same. Multiplying each data value by the same constant 5 results in the standard deviation being |c| times as large. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be 5 = 3.8 miles. Vour friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? Yes No Given 1 mile s: 1.5 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) 5 : km