Reference no: EM133853640
Questions
1. A company that manufactures halogen lamp sockets produces parts with an average length of 385 mm and a standard deviation of 15 mm. To monitor production quality, they take daily samples of 21 sockets and measure their lengths using a special tool.
Calculate the lower control limit (LCL) for a control chart based on Z = 3. Round your final answer to one decimal place.
2. The police department analyzes crime frequency data across different sectors in its jurisdiction. Each sector contains 1,000 people. Over the past year, crime incidents in each of the 10 sectors are recorded as follows:
[6, 25, 5, 11, 21, 17, 10, 25, 7, 34]
Determine the upper control limit (UCL) using Z = 3. Multiply the result by 1,000 and round down to the nearest whole number. For instance, if your result is 0.0456789, enter 45.
3. A plant manager collected 11 consecutive samples of 25 brake hoses each, recording the average length of each sample (in cm) as:
40, 39.8, 39.6, 39.4, 39.2, 39, 39.2, 39.4, 39.6, 39.8, 40
The population standard deviation is σ = 1 cm.
Using Z = 3, calculate the control chart limits. Based on your findings, is the production process statistically in control? Choose the most appropriate conclusion.
4. O'Vidia manufactures computer chips intended for use by the space agency. The chips are expected to last between 3,000 and 3,600 processing hours. The actual longevity of these chips follows a normal distribution with a mean of 3,300 hours and a standard deviation of 100 hours.
Calculate the process capability index (Cp) for the chips. Round your answer to one decimal place.
5. Xeta, a social network platform, outsources the review of images and posts to ensure they meet platform guidelines. To monitor one subcontractor (FestImage), Xeta reviewed 14 days of samples, each with 220 review requests per day. The number of incorrect assessments per day was recorded. Eight months later, the process was repeated under the same conditions.
Evaluate whether FestImage's review process was under control before and after the quality improvement efforts. Also, assess whether those efforts were effective. What might have occurred between the first and second review periods?
6. Rose Noire's "XXL 90% cocoa" chocolate bars are labeled as weighing 500 g. If the actual weight falls short of that label, the company risks fines for non-compliance with labeling standards. The chocolate-pouring machine fills each mold following a normal distribution with a standard deviation of 5 g. Initially, the machine is calibrated to pour an average of 510 g, with a maximum capacity of 540 g.
a) Estimate the proportion of bars that will exceed 500 g. Round your answer to four decimal places.
b) To check production control, a sample of 5 bars per hour is taken. Calculate the Z = 3 control limits (lower and upper). Round both to one decimal place.
c) In an effort to reduce waste, management lowers the target fill level to 506 g, while still meeting the compliance rate from part (a). What should be the new standard deviation for the updated machine to maintain this standard? Round your answer to one decimal place.