1. ## Standard deviation

1) The yearly service contract for the food fryer estimates a mean annual cost of $140 and a standard deviation of$40. What is the expected value and standard deviation for the total cost for the service contracts for the freezer and the food fryer.

freezer SD= $26.22 To find the SD= Var(freezer+fryer)=(26.22)^2 + (40)^2 =$47.83

Why do I need to square the values to add them together? Why can we not just add the to Standard Deviations?

2) Which service contract should the restaurant expect to cost more each year? How much more? with what Standard deviation

E(fryer-freezer)= 140-136.55= 3.45 more

SD fryer = $40 SD freezer =$26.22

I am told Var(fryer-freezer)= $47.83 How can this be if I want to subtract the values? Why Do we not subtract the variance for each and then take the square root? Why would the Standard Deviations be the same for both questions? Thank you 2. Originally Posted by IDontunderstand 1) The yearly service contract for the food fryer estimates a mean annual cost of$140 and a standard deviation of $40. What is the expected value and standard deviation for the total cost for the service contracts for the freezer and the food fryer. freezer SD=$26.22

To find the SD= Var(freezer+fryer)=(26.22)^2 + (40)^2 = $47.83 Why do I need to square the values to add them together? Why can we not just add the to Standard Deviations? 2) Which service contract should the restaurant expect to cost more each year? How much more? with what Standard deviation E(fryer-freezer)= 140-136.55= 3.45 more SD fryer =$40 SD freezer = $26.22 I am told Var(fryer-freezer)=$47.83 How can this be if I want to subtract the values? Why Do we not subtract the variance for each and then take the square root? Why would the Standard Deviations be the same for both questions?

Thank you
Consult your textbook for a proof of $Var(X \pm Y) = \sigma_X^2 + \sigma_Y^2$ (when X and Y are independent random variables). Alternatively, use Google to find the proof - there are any number of websites that give it.