A component part for a motorcycle is manufactured by an investment casting process. The air vent opening on this casting is an important functional parameter of the part. The results for five samples are given in the table. The values given have been coded using the last two digits of the dimension   Sample Air vent opening diameter (in mm             1 58 61 54 60 2 61 55 58 62 3 66 60 59 55 4 53 57 58 64 5 65 63 79 61     The sample data for a subsequent week had the values: 64, 69, 62, and 78. What conclusion can be reached about the state of the process?

A component part for a motorcycle is manufactured by an investment casting process. The air vent opening on this casting is an important functional parameter of the part. The results for five samples are given in the table. The values given have been coded using the last two digits of the dimension   Sample Air vent opening diameter (in mm             1 58 61 54 60 2 61 55 58 62 3 66 60 59 55 4 53 57 58 64 5 65 63 79 61       Determine the central line and control limits for the range and mean charts, and discuss whether or not  the process is in statistical control.

K The school board is trying to evaluate a new math program introduced to second-graders in five elementary schools across the county this year. A sample of the student scores on standardized math tests in each elementary school yielded the following data: School A 4 C E No. of Test Errors 48 21 32 40 52 For the test errors, the c-chart with control limits that contain 99.73% of the random variation in test scores is: UCL = errors (round your response to two decimal places).

Arana is a company that produces homemade Rotini pasta. They use statistical process control to monitor the manufacturing process. The company collects five samples, each containing six packs of pasta. Below is the sample data, but the standard deviation of the process output is unknown. If an R chart is created using three-sigma limits (i.e., z = 3) to monitor the variability of products, what would be the upper control limit for this R chart? Sample 1 Sample 2 Sample 3 Pack 1 452.3 451.6 448.6 Sample 4 454.7 Sample 5 448.9 7.614 9.328 11.653 13.427 Pack 2 452.8 451.2 455.6 451.7 453.4 Pack 3 456 454.6 456.5 451 456.7 Pack 4 457.2 455.3 451.9 452.6 456.3 Pack 5 457.8 452.2 455.6 454.7 452.4 Pack 6 451.8 451.9 448.3 458.4 456

6-9. A process that produces computer chips has a mean of .04 defective chip and a standard deviation of .003 chip. The allowable variation is from .03 to .05 defective. (a) Compute the capability index for the process (b) Is the process capable?

The school board is trying to evaluate a new math program introduced to​ second-graders in five elementary schools across the county this year. A sample of the student scores on standardized math tests in each elementary school yielded the following​ data: School No. of Test Errors A 75 B 38 C 42 D 47 E 61   For the test​ errors, the c​-chart with control limits that contain​ 99.73% of the random variation in test scores​ is: Part 2 UCLc ​= enter your response here errors ​(round your response to two decimal​ places).   b) Has the process been in​ control? c) If the sample size were 20 ​instead, how would your limits and conclusions​ change? UCLp​= ________​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). LCLp​= ________​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places).