A vending machine automatically pours soft drinks into cups. The amount of soft
ID: 3217357 • Letter: A
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. (Round your answer to two decimal places.)
(b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.)
(c) The machine has just been loaded with 876 cups. How many of these do you expect will overflow when served?
Area Under a Normal Curve 2.359% 13.59% 349% 34% 13.5% 2.35% 30 689% 95% 99.79%Explanation / Answer
Solution:
Here Mean is 7.6 oz with a standard deviation of 0.4 ounces.
This means that "mew" + "sigma" is 8.0oz The probability that the machine will overflow an 8.0oz cup lies above this place on the curve. If you look at the curve u+o has 13.5% and 2.35% to the right of it.
13.5+2.35= 15.85%
The probability that the machine will not overflow is simply: 100% - (the probability of the cup overflowing), so 100%-15.85% = 84.15%
Next, with 884 cups, to find how many of these will overflow, you need to know what 15.85% of 884 is.
So, 876 * 0.1585 = 138.85 cups