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 7.2 ounces and standard deviation of 0.4 ounce. Examine the figure below and answer the following questions.A graph titled "Area Under a Normal Curve" with a bell-shaped, continuous, and symmetric curve above the horizontal axis is given.There are 7 equally spaced labels on the axis; from left to right they are: μ − 3σ, μ − 2σ, μ − σ, μ, μ + σ, μ + 2σ, and μ + 3σ.The curve enters the viewing window just above the axis at μ − 3σ, reaches a peak at μ, and exits the viewing window just above the axis at μ + 3σ.There are 6 regions under the curve and above the axis labeled with percentage values. Regions with the same percentage value have the same color.The area under the curve between μ − 3σ and μ − 2σ is labeled 2.35%.The area under the curve between μ − 2σ and μ − σ is labeled 13.5%.The area under the curve between μ − σ and μ is labeled 34%.The area under the curve between μ and μ + σ is labeled 34%.The area under the curve between μ + σ and μ + 2σ is labeled 13.5%.The area under the curve between μ + 2σ and μ + 3σ is labeled 2.35%.68% of the area under the curve lies between μ − σ and μ + σ.95% of the area under the curve lies between μ − 2σ and μ + 2σ.99.7% of the area under the curve lies between μ − 3σ and μ + 3σ.(a)Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to three 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 840 cups. How many of these cups do you expect will overflow when served? Round your answer to a whole number.about cups

The mean of 7.2 ounces and standard deviation of 0.4 ounce. The one standard deviation limits are,…

Answered: (a) Estimate the probability that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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 7.2 ounces and standard deviation of 0.4 ounce. Examine the figure below and answer the following questions.

A graph titled "Area Under a Normal Curve" with a bell-shaped, continuous, and symmetric curve above the horizontal axis is given.

There are 7 equally spaced labels on the axis; from left to right they are: μ − 3σ, μ − 2σ, μ − σ, μ, μ + σ, μ + 2σ, and μ + 3σ.
The curve enters the viewing window just above the axis at μ − 3σ, reaches a peak at μ, and exits the viewing window just above the axis at μ + 3σ.
There are 6 regions under the curve and above the axis labeled with percentage values. Regions with the same percentage value have the same color.

The area under the curve between μ − 3σ and μ − 2σ is labeled 2.35%.
The area under the curve between μ − 2σ and μ − σ is labeled 13.5%.
The area under the curve between μ − σ and μ is labeled 34%.
The area under the curve between μ and μ + σ is labeled 34%.
The area under the curve between μ + σ and μ + 2σ is labeled 13.5%.
The area under the curve between μ + 2σ and μ + 3σ is labeled 2.35%.

68% of the area under the curve lies between μ − σ and μ + σ.
95% of the area under the curve lies between μ − 2σ and μ + 2σ.
99.7% of the area under the curve lies between μ − 3σ and μ + 3σ.

(a)

Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to three 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 840 cups. How many of these cups do you expect will overflow when served? Round your answer to a whole number.

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