Question

A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6 ounces and standard deviation of 0.4 ounce. Examine the figure below and answer the following questions. a) Estimate the probability that the machine will overflow an 8-ounce cup. (b) Estimate the probability that the machine will not overflow an 8-ounce cup. (c) The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

Answer 1

a) P(X > 8)

= P(z > (8 - 7.6)/0.4)

= P(z > 1)

= 0.1587

b) P(Not overflow) = 1 - 0.1587 = 0.8413

c) Expected number of cups overflown = 850*0.1587 = 135