Explanation Given: The length of the precision part of the manufacturing process is a normal random variable with mean deviation of μ = 100 millimeters and the standard deviation of σ = 2 millimeters. The components will be rejected when the deviation is more than 5 millimeters from the mean deviation of 100 millimeters. Formula used: “The standard normal variable: z = X − μ σ , where µ is the mean and σ is the standard deviation.” Calculation: The deviation that are more than the mean deviation of 5 millimeters that is 100 + 5 = 105 will be rejected and the less than the mean deviation of 100 that is 100 − 5 = 95 will also be rejected. Find the probability of the rejected parts. That is, P ( X ≤ 95 ) and P ( 105 ≤ X ) . In order to find the probability P ( X ≤ 95 ) , first find the standard normal variable z using the above mentioned formula. z = 95 − 100 2 = − 5 2 = − 2.5 Thus, the probability P ( X ≤ 95 ) becomes P ( z ≤ − 2.5 ) . In order to find the probability P ( 105 ≤ X ) , first find the standard normal variable z using the above mentioned formula z = 105 − 100 2 = 5 2 = 2

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Chapter 11.4, Problem 77E

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To find: The percentage of parts to be rejected.

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Chapter 11.4, Problem 76E

Chapter 11.4, Problem 78E

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Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The percentage of parts to be rejected.

Solution Summary: The author explains that the percentage of parts to be rejected is 1.24%. The normal curve is symmetric with respect to the vertical line through Figure 1.

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