Answer Happy

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. Area Under a Normal Curve 2.35% 13.5% 34% м-30 м - 2 μ-0 34% 13.5% 2.35% f 68% 95% 99.7% μ+σ μ+ 20 μ + 30 (a) Estimate the probability that the machine will overflow an 8-ounce cup. Q (b) Estimate the probability that the machine will not overflow an 8-ounce cup. (c) The machine has just been loaded with 675 cups. How many of these cups do you expect will overflow when served?
(a) Estimate the probability that the machine will overflow an 8-ounce cup. It is given that a vending machine dispenses a mean of 7.6 ounces with a standard deviation of 0.4 ounce. For the vending machine to overflow an 8-ounce cup, the machine must pour more than 8 - 7.6 = 0.4 ounces greater than the mean. This amount is 0.1587 X standard deviation(s) from the mean.