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In: Math

Each statement represents a scenario in which a linear transformation has occurred. Select the correct statements...

Each statement represents a scenario in which a linear transformation has occurred. Select the correct statements regarding the standard deviation of the variables after the linear transformation.

-A malfunctioning machine produces a particular part with a mean length of 30 in and a standard deviation of 1 in. If a second part with a consistent length of 2 in is added to the end of the first part, then the standard deviation of the total part lengths will be equal to 3 in.

-The distribution of heights of adult males in the United States has a standard deviation of 4 in. If these heights in inches are converted to feet, then the standard deviation of heights will be 13 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 to raise its prices by 50%, then the standard deviation of the new prices will be $6.

-For a particular set of daily TV-watching data, the average number of hours of TV watched per day is 3 hrs, and the standard deviation is 2 hrs. If these daily results are translated to weekly TV-watching results, the standard deviation for the total number of hours of TV watched per week remains unchanged from the standard deviation of 2 hrs.

-The final times (in minutes) for a high school foot race are distributed with a mean of 20 min and a standard deviation of 4 min. The person charged with keeping track of time realized that he started the stopwatch 1 minlate for all runners. Thus, he decides to add 1 min to everyone's time. The standard deviation of the new final times will remain unchanged at 4 min.

Solutions

Expert Solution

#1 ) Incorrect.

Standard deviation influenced by outliers one value could contribute largely to the results of the standard deviation.

We are given that the average of first part is 30inches, it means most of part lengths are close to 30inches. Therefore If a second part with a consistent length of 2 in is added to the end of the first part, it would be work as an outlier, so the standard deviation of the total part lengths will be large.

#2) Incorrect , The standard deviation of heights will be 4*12 =48 ft ( standard deviation is only affected by a change in scale.)

#3) Correct !.

Since standard deviation is only affected by a change in scale , so raise in prices by 50% means we have to multiply by 0.5 to the standard deviation and add that product to the standard deviation , it will give the new standard deviation after rasing the prices by 50%

So 0.5*$4 = $2 , $4+$2 = $6

#4) Incorrect .

If these daily results are translated to weekly TV-watching results,then we need to multiply by standard deviation by 7 ( 7 days in a week )

So standard deviation = 2*7 = 14 hrs

$5) Correct!

standard deviation is only affected by a change in scale ( multiplication and division ) and not by the change of origin ( adding or subtracting ) .

milcah answered 6 months ago
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