A coffee-vending machine is set to dispense amounts of coffee per cup that follows a normal distribution with a mean of 200 mL and a standard deviation of 10 mL. Let the random variable X be the amount of coffee (in mL) per cup. a. What is the probability that a randomly selected cup will contain more than 225 mL of coffee as dispensed by the machine? b. What proportion of the cups will contain anywhere between 198 and 215 mL of coffee?

The normal distribution is a continuous random variable that has a parameter μ and σ. If a normal…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A coffee-vending machine is set to dispense amounts of coffee per cup that follows a normal distribution with a mean of 200 mL and a standard deviation of 10 mL. Let the random variable X be the amount of coffee (in mL) per cup.

a. What is the probability that a randomly selected cup will contain more than 225 mL of coffee as dispensed by the machine?

b. What proportion of the cups will contain anywhere between 198 and 215 mL of coffee?

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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