Each statement represents a scenario in which a lineartransformation has occurred. Select the correct statementsregarding the standard deviation of the variables after the lineartransformation.
-A malfunctioning machine produces a particular part with a meanlength of 30 in and a standard deviation of 1 in. If a second partwith a consistent length of 2 in is added to the end of the firstpart, then the standard deviation of the total part lengths will beequal to 3 in.
-The distribution of heights of adult males in the United Stateshas a standard deviation of 4 in. If these heights in inches areconverted to feet, then the standard deviation of heights will be13 ft.
-Prices on a menu at a particular restaurant have a mean cost of$10 and a standard deviation of $4. If the restaurant decides toraise its prices by 50%, then the standard deviation of the newprices will be $6.
-For a particular set of daily TV-watching data, the averagenumber of hours of TV watched per day is 3 hrs, and the standarddeviation is 2 hrs. If these daily results are translated to weeklyTV-watching results, the standard deviation for the total number ofhours of TV watched per week remains unchanged from the standarddeviation of 2 hrs.
-The final times (in minutes) for a high school foot race aredistributed with a mean of 20 min and a standard deviation of 4min. The person charged with keeping track of time realized that hestarted the stopwatch 1 minlate for all runners. Thus, he decidesto add 1 min to everyone's time. The standard deviation of the newfinal times will remain unchanged at 4 min.
