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High School Math Calculus PRECALCULUS:GRAPHICAL,...-NASTA ED.

The percentage of the ball bearings that will be rejected. The percentage of ball bearings that will be rejected is about 5%. Given: The standard deviation of the diameter of the ball bearings produced = 0.05 mm. The specified value of deviation from the diameter where output is rejected is = 0.1 mm. Concept used: In a normal distribution , the percentage of data within one standard deviation of the mean is about 68%, the percentage of data within two standard deviations of the mean is about 95%, and the percentage of data within three standard deviations of the mean is about 99.7%. The Z score of a data value is the number of standard deviations from the mean Calculation: The diameter of the ball bearings produced has to be within 0.1 mm from the mean, which is nothing but two times the standard deviation. Thus the diameter of the ball bearings produced has to be within 0.1 mm of the mean or within two standard deviations of the mean. According to the empirical rule within two standard deviations from the mean, the percentage of data is about 95%. Thus the percentage of the data which is not within two standard deviations of the mean is = 100 % − 95 % = 5 % Conclusion: The percentage of the ball bearings whose diameter deviates more than 0.1 mm from the mean and get rejected is about 5%.

The percentage of the ball bearings that will be rejected. The percentage of ball bearings that will be rejected is about 5%. Given: The standard deviation of the diameter of the ball bearings produced = 0.05 mm. The specified value of deviation from the diameter where output is rejected is = 0.1 mm. Concept used: In a normal distribution , the percentage of data within one standard deviation of the mean is about 68%, the percentage of data within two standard deviations of the mean is about 95%, and the percentage of data within three standard deviations of the mean is about 99.7%. The Z score of a data value is the number of standard deviations from the mean Calculation: The diameter of the ball bearings produced has to be within 0.1 mm from the mean, which is nothing but two times the standard deviation. Thus the diameter of the ball bearings produced has to be within 0.1 mm of the mean or within two standard deviations of the mean. According to the empirical rule within two standard deviations from the mean, the percentage of data is about 95%. Thus the percentage of the data which is not within two standard deviations of the mean is = 100 % − 95 % = 5 % Conclusion: The percentage of the ball bearings whose diameter deviates more than 0.1 mm from the mean and get rejected is about 5%.

PRECALCULUS:GRAPHICAL,...-NASTA ED.

PRECALCULUS:GRAPHICAL,...-NASTA ED.

10th Edition

ISBN: 9780134672090

Author: Demana

Publisher: PEARSON

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Expert Solution & Answer

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.

Chapter 10.3, Problem 59E

Solution

To calculate: The percentage of the ball bearings that will be rejected.

The percentage of ball bearings that will be rejected is about 5%.

Given:

The standard deviation of the diameter of the ball bearings produced =0.05 mm.

The specified value of deviation from the diameter where output is rejected is =0.1 mm.

Concept used:

In a normal distribution, the percentage of data within one standard deviation of the mean is about 68%, the percentage of data within two standard deviations of the mean is about 95%, and the percentage of data within three standard deviations of the mean is about 99.7%. The Z score of a data value is the number of standard deviations from the mean

Calculation:

The diameter of the ball bearings produced has to be within 0.1 mm from the mean, which is nothing but two times the standard deviation. Thus the diameter of the ball bearings produced has to be within 0.1 mm of the mean or within two standard deviations of the mean. According to the empirical rule within two standard deviations from the mean, the percentage of data is about 95%. Thus the percentage of the data which is not within two standard deviations of the mean is =100%−95%=5%

Conclusion:

The percentage of the ball bearings whose diameter deviates more than 0.1 mm from the mean and get rejected is about 5%.

Chapter 10.3, Problem 58E

Chapter 10.3, Problem 60E

Chapter 10 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 10.1 - Prob. 1QR Ch. 10.1 - Prob. 2QR Ch. 10.1 - Prob. 3QR Ch. 10.1 - Prob. 4QR Ch. 10.1 - Prob. 5QR Ch. 10.1 - Prob. 6QR Ch. 10.1 - Prob. 7QR Ch. 10.1 - Prob. 8QR Ch. 10.1 - Prob. 9QR Ch. 10.1 - Prob. 10QR

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - Prob. 59E Ch. 10.1 - Prob. 60E Ch. 10.1 - Prob. 61E Ch. 10.1 - Prob. 62E Ch. 10.2 - Prob. 1QR Ch. 10.2 - Prob. 2QR Ch. 10.2 - Prob. 3QR Ch. 10.2 - Prob. 4QR Ch. 10.2 - Prob. 5QR Ch. 10.2 - Prob. 6QR Ch. 10.2 - Prob. 7QR Ch. 10.2 - Prob. 8QR Ch. 10.2 - Prob. 9QR Ch. 10.2 - Prob. 10QR Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - 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Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - Prob. 20E Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Prob. 31E Ch. 10.3 - Prob. 32E Ch. 10.3 - Prob. 33E Ch. 10.3 - Prob. 34E Ch. 10.3 - Prob. 35E Ch. 10.3 - Prob. 36E Ch. 10.3 - Prob. 37E Ch. 10.3 - Prob. 38E Ch. 10.3 - Prob. 39E Ch. 10.3 - Prob. 40E Ch. 10.3 - Prob. 41E Ch. 10.3 - Prob. 42E Ch. 10.3 - Prob. 43E Ch. 10.3 - Prob. 44E Ch. 10.3 - Prob. 45E Ch. 10.3 - Prob. 46E Ch. 10.3 - Prob. 47E Ch. 10.3 - Prob. 48E Ch. 10.3 - Prob. 49E Ch. 10.3 - Prob. 50E Ch. 10.3 - Prob. 51E Ch. 10.3 - Prob. 52E Ch. 10.3 - Prob. 53E Ch. 10.3 - Prob. 54E Ch. 10.3 - Prob. 55E Ch. 10.3 - Prob. 56E Ch. 10.3 - Prob. 57E Ch. 10.3 - Prob. 58E Ch. 10.3 - Prob. 59E Ch. 10.3 - Prob. 60E Ch. 10.4 - Prob. 1QR Ch. 10.4 - Prob. 2QR Ch. 10.4 - Prob. 3QR Ch. 10.4 - Prob. 4QR Ch. 10.4 - Prob. 5QR Ch. 10.4 - Prob. 6QR Ch. 10.4 - Prob. 7QR Ch. 10.4 - Prob. 8QR Ch. 10.4 - Prob. 9QR Ch. 10.4 - Prob. 10QR Ch. 10.4 - Prob. 1E Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - Prob. 7E Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.4 - Prob. 11E Ch. 10.4 - Prob. 12E Ch. 10.4 - Prob. 13E Ch. 10.4 - Prob. 14E Ch. 10.4 - Prob. 15E Ch. 10.4 - Prob. 16E Ch. 10.4 - Prob. 17E Ch. 10.4 - Prob. 18E Ch. 10.4 - Prob. 19E Ch. 10.4 - Prob. 20E Ch. 10.4 - Prob. 21E Ch. 10.4 - Prob. 22E Ch. 10.4 - Prob. 23E Ch. 10.4 - Prob. 24E Ch. 10.4 - Prob. 25E Ch. 10.4 - Prob. 26E Ch. 10.4 - Prob. 27E Ch. 10.4 - Prob. 28E Ch. 10.4 - Prob. 29E Ch. 10.4 - Prob. 30E Ch. 10.4 - Prob. 31E Ch. 10.4 - Prob. 32E Ch. 10.4 - Prob. 33E Ch. 10.4 - Prob. 34E Ch. 10.4 - Prob. 35E Ch. 10.4 - Prob. 36E Ch. 10.4 - Prob. 37E Ch. 10.4 - Prob. 38E Ch. 10.4 - Prob. 39E Ch. 10.4 - Prob. 40E Ch. 10.4 - Prob. 41E Ch. 10.4 - Prob. 42E Ch. 10.4 - Prob. 43E Ch. 10.4 - Prob. 44E Ch. 10.4 - Prob. 45E Ch. 10.4 - Prob. 46E Ch. 10.4 - Prob. 47E Ch. 10.4 - Prob. 48E Ch. 10.4 - Prob. 49E Ch. 10.4 - Prob. 50E Ch. 10.4 - Prob. 51E Ch. 10.4 - Prob. 52E Ch. 10.4 - Prob. 53E Ch. 10.4 - Prob. 54E Ch. 10.4 - Prob. 55E Ch. 10.4 - Prob. 56E Ch. 10.5 - Prob. 1QR Ch. 10.5 - Prob. 2QR Ch. 10.5 - Prob. 3QR Ch. 10.5 - Prob. 4QR Ch. 10.5 - Prob. 5QR Ch. 10.5 - Prob. 6QR Ch. 10.5 - Prob. 7QR Ch. 10.5 - Prob. 8QR Ch. 10.5 - Prob. 9QR Ch. 10.5 - Prob. 10QR Ch. 10.5 - Prob. 1E Ch. 10.5 - Prob. 2E Ch. 10.5 - Prob. 3E Ch. 10.5 - Prob. 4E Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Prob. 9E Ch. 10.5 - Prob. 10E Ch. 10.5 - Prob. 11E Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Prob. 17E Ch. 10.5 - Prob. 18E Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Prob. 21E Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10.5 - Prob. 27E Ch. 10.5 - Prob. 28E Ch. 10.5 - Prob. 29E Ch. 10.5 - Prob. 30E Ch. 10.5 - Prob. 31E Ch. 10.5 - Prob. 32E Ch. 10.5 - Prob. 33E Ch. 10.5 - Prob. 34E Ch. 10.5 - Prob. 35E Ch. 10.5 - Prob. 36E Ch. 10.5 - Prob. 37E Ch. 10.5 - Prob. 38E Ch. 10.5 - Prob. 39E Ch. 10.5 - Prob. 40E Ch. 10.5 - Prob. 41E Ch. 10.5 - Prob. 42E Ch. 10.5 - Prob. 43E Ch. 10.5 - Prob. 44E Ch. 10.5 - Prob. 45E Ch. 10.5 - Prob. 46E Ch. 10.5 - Prob. 47E Ch. 10.5 - Prob. 48E Ch. 10.5 - Prob. 49E Ch. 10.5 - Prob. 50E Ch. 10.5 - Prob. 51E Ch. 10.5 - Prob. 52E Ch. 10.5 - Prob. 55E Ch. 10.5 - Prob. 56E Ch. 10.5 - Prob. 59E Ch. 10.5 - Prob. 60E Ch. 10 - Prob. 1RE Ch. 10 - Prob. 2RE Ch. 10 - Prob. 3RE Ch. 10 - Prob. 4RE Ch. 10 - Prob. 5RE Ch. 10 - Prob. 6RE Ch. 10 - Prob. 7RE Ch. 10 - Prob. 8RE Ch. 10 - Prob. 9RE Ch. 10 - Prob. 10RE Ch. 10 - Prob. 11RE Ch. 10 - Prob. 12RE Ch. 10 - Prob. 13RE Ch. 10 - Prob. 14RE Ch. 10 - Prob. 15RE Ch. 10 - 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