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The length of an injection-molded plastic case that holds
Chapter 4, Problem 195SE(choose chapter or problem)
The length of an injection-molded plastic case that holds magnetic tape is normally distributed with a length of 90.2 millimeters and a standard deviation of 0.1 millimeter.
(a) What is the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters?
(b) What should the process mean be set at to obtain the highest number of parts between 89.7 and 90.3 millimeters?
(c) If parts that are not between 89.7 and 90.3 millimeters are scrapped, what is the yield for the process mean that you selected in part (b)? Assume that the process is centered so that the mean is 90 millimeters and the standard deviation is 0.1 millimeter. Suppose that 10 cases are measured, and they are assumed to be independent.
(d) What is the probability that all 10 cases are between 89.7 and 90.3 millimeters?
(e) What is the expected number of the 10 cases that are between 89.7 and 90.3 millimeters?
Questions & Answers
QUESTION:
The length of an injection-molded plastic case that holds magnetic tape is normally distributed with a length of 90.2 millimeters and a standard deviation of 0.1 millimeter.
(a) What is the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters?
(b) What should the process mean be set at to obtain the highest number of parts between 89.7 and 90.3 millimeters?
(c) If parts that are not between 89.7 and 90.3 millimeters are scrapped, what is the yield for the process mean that you selected in part (b)? Assume that the process is centered so that the mean is 90 millimeters and the standard deviation is 0.1 millimeter. Suppose that 10 cases are measured, and they are assumed to be independent.
(d) What is the probability that all 10 cases are between 89.7 and 90.3 millimeters?
(e) What is the expected number of the 10 cases that are between 89.7 and 90.3 millimeters?
ANSWER:
Step 1 of 7
The Mean,
The standard deviation,
Suppose that X is a normal random variable with mean 
where Z is a standard normal random variable, and
is the z-value obtained by standardizing X. The probability is obtained by using Appendix Table III.