# Expectation algebra

It costs a total of 17c for each piece of toast. Calculate the mean and variance for cost per student of toast with spreads. (Know mean number of pieces of toast is 1.71 and variance is 1,106,

And following on from that: plates cost 12c per student. Every student has 1 plate and plates are not reused. Calculate the mean and standard deviation for cost per student for a student for plate plus spreads.
Thanks you.

Welcome to the forum! Can you specify what sort of help do you require with this problem?

I can get the mean but the variance or SD

Sorry, meant can’t get variance in the first or sd in the second

If each student eats 1.71 pieces of toast on average and each toast costs \$0.17 then the mean price (or expected value) will be:

E(0.17t)=0.17*1.71=0.2907 (\$)

To find the variance for the price we need to multiply the average amount of toast by the squared price of each piece of toast (remember, when we find variance we square the differences so we need to square the constant as well):

Var(0.17t)=0.17^2*1.106=0.032

Standard deviation is a square root of variance which is \$0.179.

Or you could first find the standard deviation for the toast as a square root of variance SQRT(1.106)= 1.05 (which practically means that about 68% of students eat on average 1.71 plus minus 1.05 pieces of toast). So they spend 0.17*1.71=0.2907 with standard deviation 1.05 * 0.17=0.179 (\$)

When you add a plate to the equation the average price would increase by the price of the plate (\$0.12) so

E(0.17t+0.12)=0.2907+0.12=0.4107 (\$)

The variance and standard deviation won’t change when you add a fixed price (of the plate) as they only depend on the amount of toast bought.

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