A manufacturing company produces metal pipes with a desired width of 2.5 cm. Due to machine error, the pipes vary somewhat from this target. The company takes a sample of 100 pipes produced. The observed mean pipe width was approximately 2.502 and the sample standard deviation was 0.00932. The company also determined that the cutoff measurement for the widest 2.5% of pipes that were observed is 2.519. The research department of the company believes that the width of the pipes is normally distributed, with a mean of 2.5 cm and a standard deviation of 0.01. If that is the case, what should the cutoff be for the widest 2.5% of pipes be? Using any of the information above, do you think the research department’s beliefs about the distribution of the tube widths are plausible? Explain your reasoning. (Hint: How do the observed mean, standard deviation, and percentile cutoffs compare to the research’s teams baseline assumptions?) The box-and-whisker plot below represents the tube width data from the previous problem. One value is represented as a point. What is the significance of that? What does the line drawn through the blue box represent? What does the “x” inside of the box represent? What is the significance of the fact that the line and the “x” are in different places?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.CT: Chapter Test

Problem 16CT: How many six-digit license plates can be made if no plate begins with 0 or 1?

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A manufacturing company produces metal pipes with a desired width of 2.5 cm. Due to machine error, the pipes vary somewhat from this target. The company takes a sample of 100 pipes produced. The observed mean pipe width was approximately 2.502 and the sample standard deviation was 0.00932. The company also determined that the cutoff measurement for the widest 2.5% of pipes that were observed is 2.519.

The research department of the company believes that the width of the pipes is normally distributed, with a mean of 2.5 cm and a standard deviation of 0.01. If that is the case, what should the cutoff be for the widest 2.5% of pipes be?

Using any of the information above, do you think the research department’s beliefs about the distribution of the tube widths are plausible? Explain your reasoning. (Hint: How do the observed mean, standard deviation, and percentile cutoffs compare to the research’s teams baseline assumptions?)

The box-and-whisker plot below represents the tube width data from the previous problem.

One value is represented as a point. What is the significance of that?
What does the line drawn through the blue box represent?
What does the “x” inside of the box represent?
What is the significance of the fact that the line and the “x” are in different places?

2.540
2.530
2.520
2.510
2.500
2.490
2.480
2.470
X

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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