Question

A fastfood chain's softdrink machine is calibrated so that it disperses an average of 225 milliliters per cup. The amount of drink is normally distributed with a standard deviation equal to 15 milliliters.

Answer 1

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A fast-food chain's soft-drink machine is calibrated so that it disperses an average of 225 milliliters per cup. The amount of drink is normally distributed with a standard deviation equal to 15 milliliters. How many cups will probably overflow if 255- milliliter cups are used for the next 1000 drinks?

Solution:

Let X represent the amount of drink distributed.

$\mu = 225 \\ \sigma=15$

The number of cups that will probably overflow if 230-milliliter cups are used for the next 1000 drinks

$P(X>230) = 1 -P(X<230) \\ = 1 -P(Z< \frac{255-225}{15}) \\ = 1 -P(Z< \frac{30}{15}) \\ = 1 -P(Z<2) \\ = 1 -0.9772 \\ = 0.0228 \\ E(X) = n \times P \\ =1000 \times 0.0228 \\ = 22.8 ≈ 23$

Hence, 23 cups will overflow.