### Process Capability and Six Sigma Analysis for Leah’s Toys**a. Process Capability Ratio**- **Problem Statement:** What is the process capability ratio, assuming upper and lower tolerance limits of 3.5 and 2.5 ounces? Is Leah's able to meet the tolerance limits 99.7% of the time? Explain.- **Explanation:** The process capability ratio (Cp) measures how well a process can produce output within given specification limits. It is calculated using the formula: \[ Cp = \frac{\text{Upper Tolerance Limit} - \text{Lower Tolerance Limit}}{6\sigma} \] To meet the tolerance limits 99.7% of the time requires the process to fit within the specifications with minimal variability.**b. Required Standard Deviation for 99.7% Compliance**- **Problem Statement:** What would the standard deviation have to be to exactly meet the tolerance limits 99.7% of the time?- **Explanation:** To determine the required standard deviation ($\sigma$) for the process to meet the tolerance limits with 99.7% compliance, you should set the specification range equal to $6\sigma$, following a normal distribution coverage of 99.7%. This relationship ensures that the process variability aligns with the specified limits.**c. Six Sigma Quality Level Assessment**- **Problem Statement:** Suppose Leah’s Toys invests in process improvements that lower the standard deviation to just 0.10 ounces. Is this enough for Leah's to achieve Six Sigma quality levels with regard to the weight of the balls? Explain.- **Explanation:** Achieving Six Sigma quality typically means that the process standard deviation is small enough to fit within the specification limits at 12 times ($12\sigma$) the range (including the target mean). With a standard deviation of 0.10 ounces, evaluate whether the process meets the Six Sigma criteria by verifying that this covers the specification limits with the desired low defect rate (3.4 defects per million opportunities). **Leah's Toys: Rubber Ball Production**Leah's Toys manufactures rubber balls. The current production process yields balls with an average weight of 3 ounces and a standard deviation of 0.25 ounces.*Educational Note:*- **Average Weight:** This is the mean weight of the rubber balls produced, which is 3 ounces.- **Standard Deviation:** This measures how much variation or dispersion exists from the average weight. Here, the standard deviation is 0.25 ounces, indicating that the weights of the balls tend to vary by this amount from the mean weight.

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Answered: 4. Leah's Toys makes rubber balls. The…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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According to United States Department of Agriculture, the average retail price of conventional whole milk at New York City in the year 2020 (up to November 2020 considered) is $3.92 per gallon. The standard deviation in the retail prices in the year 2020 (up to November 2020 considered) is $0.084. You are given a task of selecting randomly a sample of 85 milk bottles (whole milk of 1 gallon volume). a. Calculate µx̅ and σx̅. b. What is the approximate probability that the sample has a mean retail price that exceeds $4.05? c. What is the approximate probability that the sample has a mean retail price between $3.91 and $3.94?
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 42 feet. Assume the population standard deviation is 4.7 feet. The mean braking distance for Make B is 45 feet. Assume the population standard deviation is 4.4 feet. At a = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) rari rz (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are (Round to three decimal places as needed. Use a comma to separate answers as needed.)
Calculate the standard deviation of the data shown. Use technology x 27.6 2.6 13.2 8.3 8.9 3.3 Round to 2 places
The weights of a certain machine components are normally distributed with a mean of 8.85g and a standard deviation of 0.08g. Find the two weights that seperate the top 3% and the bottom 3%. These weights could serve as limits used to identify which components should be rejected. Round to the nearest hundredth of a gram. Draw a picture. Use Table A-2.
A section of highway is posted with a 55 mph speed limit. In fact, speeds of cars traveling on this section are normally distributed with mean 58 mph and standard deviation 5 mph. If the state patrol decides to ticket cars in the fastest 10 %, at what speed will they start ticketing ? Round your answer to the first decimal position.
The ages of the population of a town are Normally distributed with mean 43 and standard deviation 14. The town has a population of 5,000.How many would you expect to be aged between 22 and 57?
A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 4 stan deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have n length of 14 cm with a standard deviation of 0.05 cm. For what lengths will a bolt be destroyed? Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to one decimal place as needed.) OA. A bolt will be destroyed if the length is less than OB. A bolt will be destroyed if the length is less than OC. A bolt will be destroyed if the length is greater than OD. A bolt will be destroyed if the length is between cm and cm or greater than cm. cm. cm. cm.
Answer in 30 mins.
An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.4 mm, how many of these components should she consider to be 99% sure of knowing the mean will be within ±0.5±0.5 mm?

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4. Leah's Toys makes rubber balls. The current process is capable of producing balls that weigh, on average, 3 ounces, with a standard deviation of 0.25 ounces.