Answer to Question #259271 in Statistics and Probability for Gigi

Question

How many cups will likely overflow if 250 milliliters cups are used for the next 500 drinks?

Answer 1

Question is incomplete: Here we can frame the question like this

A soft-drink machine is regulated so that it discharges an average of 200 milliliters per cup. If the amount of drink is normally distributed with a standard deviation equal to 25 milliliters. How many cups will likely overflow if 250 milliliters cups are used for the next 500 drinks?

Solution:

Let X represent the amount of drink distributed.

$\mu = 200 \\ \sigma=25$

The number of cups that will probably overflow if 250-milliliter cups are used for the next 500 drinks

$P(X>250)=1−P(X<250) \\=1−P(Z< \frac{250-200}{25} ) \\=1−P(Z<2) \\=1−0.9772 \\=0.0228$

In case of 500 cups,

$500 \times0.0228 = 11.4\approx12$ i.e. 12 cups will overflow .