Let X be the amount of soda released by a soft-drink dispending machine into a 6-ounce cup. Assume that X is normally distrubuted with o = .25 ounces and that the average "fill" can be set by the vendor. (1) At what quantity should the average "fill" be set so that no more than .5% of the releases overflow the cup?(2) Using the average "fill" found in part (a), determine the minimal amount that will be dispensed in 99% of the cases. Soft-Drink Dispenser Let X be the amount of soda re-leased by a soft-drink dispensing machine into a 6-ounce cup. Assume that X is normally distributedwith o = .25 ounces and that the average "fill" can beset by the vendor.(a) At what quantity should the average "fill" be setso that no more than .5% of the releases overflowthe cup?(b) Using the average "fill" found in part (a), deter-mine the minimal amount that will be dispensedin 99% of the cases.

Name: Let X be the amount of soda released by a soft-drink dispending machin
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Description: Let X be the amount of soda released by a soft-drink dispending machine into a 6-ounce cup. Assume that X is normally distrubuted with o = .25 ounces and that the average "fill" can be set by the vendor. (1) At what quantity should the average "fill"

Given information: σ=0.25 a) P-value for the quantity, where no more than 0.5% of the releases overflow the cup=1-0.005=0.995 Determine the z-score using the excel formula, "=NORM.S.INV(0.995)". z0.995=2.575829304≈2.576Apply formula for the normal distribution: z=x-μσ2.576=6.0-x0.250.644=6.0-xx=6.0-0.644=5.356 The average "fill" should be set on 5.356 ounces, so that no more than 0.5% of the releases overflow the cup.P-value for the minimal amount that will be dispensed in 99% of the case=1-0.99=0.01 Determine the z-score using the excel formula, "=NORM.S.INV(0.01)". z0.01=-2.326347874≈-2.33 Apply formula for the normal distribution: z=x-μσ-2.33=x-5.3560.25-0.5825=x-5.356x=5.356-0.5825=4.7735 The minimal amount that will be dispensed in 99% of the cases is 4.7735 ounces.

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Let X be the amount of soda released by a soft-drink dispending machine into a 6-ounce cup. Assume that X is normally distrubuted with o = .25 ounces and that the average "fill" can be set by the vendor. (1) At what quantity should the average "fill" be set so that no more than .5% of the releases overflow the cup? (2) Using the average "fill" found in part (a), determine the minimal amount that will be dispensed in 99% of the cases.

Let X be the amount of soda released by a soft-drink dispending machine into a 6-ounce cup. Assume that X is normally distrubuted with o = .25 ounces and that the average "fill" can be set by the vendor. (1) At what quantity should the average "fill" be set so that no more than .5% of the releases overflow the cup? (2) Using the average "fill" found in part (a), determine the minimal amount that will be dispensed in 99% of the cases.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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(1) At what quantity should the average "fill" be set so that no more than .5% of the releases overflow the cup?

(2) Using the average "fill" found in part (a), determine the minimal amount that will be dispensed in 99% of the cases.

Soft-Drink Dispenser Let X be the amount of soda re-
leased by a soft-drink dispensing machine into a 6-
ounce cup. Assume that X is normally distributed
with o = .25 ounces and that the average "fill" can be
set by the vendor.
(a) At what quantity should the average "fill" be set
so that no more than .5% of the releases overflow
the cup?
(b) Using the average "fill" found in part (a), deter-
mine the minimal amount that will be dispensed
in 99% of the cases.

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