A vending machine that serves coffee pours a varying amount of liquid into a cup with varying mass. Assume
that the masses of the liquid and the cup are independent.
Here are summary statistics for the masses of the liquid and the cups:
Mean
Standard deviation
Liquid
HL
250 g
D = 20 g
Cup
HC = 150g
a = 10g
Let T = the total mass of a randomly selected cup filled with liquid from this machine.
Find the mean of T.
HT =
grams
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kademargain36 kademargain36 · Answer 1 · 2021-01-22T05:43:47+01:00

Answer:400

Step-by-step explanation:

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MrRoyal MrRoyal · Answer 2 · 2021-12-11T04:54:50+01:00

The mean of T is the expected weight of a selected cup filled with liquid

The mean of T is 400

The data on the table is given as:

Mean Standard Deviation

Liquid 250g 20g

Cup 150g 10g

Represent Liquid with L, and cup with C

To calculate the mean of T, we make use of the following formula for expected value

E(L + C)

Since L and C are independent random variables, then

[tex]E(L + C) = E(L) + E(C)[/tex]

Where E(L) and E(C) are the mean values of liquids and cups.

The equation becomes

[tex]E(L + C) = 250g + 150g[/tex]

[tex]E(L + C) = 400g[/tex]

Hence, the mean of T is 400