An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.74 inch. The lower and upper specification limits under which the ball bearings can operate are 0.72 inch and 0.76inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.744 inch and a standard deviation of 0.004 inch. (Round to three decimal places as needed.)What is the probability that a ball bearing is between the target and the actual mean?What is the probability that a ball bearing is between the lower specification limit and the target?What is the probability that a ball bearing is above the upper specification limit?What is the probability that a ball bearing is below the lower specification limit?Of all the ball bearings, % of the diameters are greater than what value?

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Answered: An industrial sewing machine uses ball…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.74 inch. The lower and upper specification limits under which the ball bearings can operate are 0.72 inch and 0.76inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.744 inch and a standard deviation of 0.004 inch.

(Round to three decimal places as needed.)

What is the probability that a ball bearing is between the target and the actual mean?
What is the probability that a ball bearing is between the lower specification limit and the target?
What is the probability that a ball bearing is above the upper specification limit?
What is the probability that a ball bearing is below the lower specification limit?
Of all the ball bearings, % of the diameters are greater than what value?

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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