The average weight of a group of people is 156 pounds and the SD is 25 pounds. A statistician wants to transform the weights so that the transformed weights have an average of 100 pounds and an SD of 10 pounds. Fill in the blanks; both blanks must be filled in correctly for credit.
One way for the statistician to get the transformation that she wants is to multiply all the weights by _____________, and then add _____________ to the resulting values.
To transform the weights, the statistician can use the following formula:
Transformed weight = (Original weight x Multiplication factor) + Addition factor
To calculate the multiplication factor, we need to find the ratio of the desired standard deviation (10 pounds) to the original standard deviation (25 pounds):
Multiplication factor = Desired standard deviation / Original standard deviation
Multiplication factor = 10 / 25
To calculate the addition factor, we need to consider that the transformed weights should have an average of 100 pounds. We can find the difference between the desired average (100 pounds) and the product of the multiplication factor and the original average (156 pounds):
Addition factor = Desired average - (Original average x Multiplication factor)
Addition factor = 100 - (156 x [10 / 25])
Simplifying the calculations:
Multiplication factor = 0.4
Addition factor = 100 - (156 x 0.4)
So, to transform the weights, the statistician should multiply all the weights by 0.4 and then subtract (156 x 0.4) from the resulting values.