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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 7.6 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. (b) Estimate the probability that the machine will not overflow an 8-ounce cup. (c) The machine has just been loaded with 625 cups. How many of these cups do you expect will overflow when served?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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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 7.6 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.

(b) Estimate the probability that the machine will not overflow an 8-ounce cup.

(c) The machine has just been loaded with 625 cups. How many of these cups do you expect will overflow when served?

Area Under a Normal Curve
2.35%
13.5%
34%
34%
13.5%
2.35%
u - 30 u- 20
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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