Answered: A vending machine automatically pours…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 825 cups. How many of these cups do you expect will overflow when served? cups

Area Under a Normal Curve
2.35%
13.5%
34%
34%
13.5%
2.35%
μ- 3σ μ- 2σ
u + 20 u+ 3ơ
68%
95%
99.7%

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Follow-up Question

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 = ounces greater than the mean. This amount is standard deviation(s) from the mean.