Question

A soft-drink machine is regulated so that it discharges an average of 200 mm/cup. Of the amount of drink is normally distributed with a standard deviation equal to 15 mm, how many cups will probably overflow if 230 mm cups are used for the next 1000 drinks?

Answer 1

$z= \frac{x-\mu}{\sigma} = \frac{230-200}{15} = 2$

The probability of overflow if 230 cups is used

P(X>230) = P(Z>2)

= 1- P(Z<2)

= 1- 0.9772= 0.0228

by using binomial property we get

E(X)= $\eta .p$

=1000 $\times 0.0228$ = 22.8