A process is controlled with a fraction of nonconforming control chart with three-sigma limits, n=100, center line = 0.080. (a) Find the upper and lower control limits for the fraction of nonconforming chart (b) Find the equivalent control chart for the number of nonconforming. (c) Use the correct approximation to find the probability of a type II error if the process fraction of nonconforming shifts to 0.2 (d) What is the probability of detecting the shift in part c by at most the fourth sample after the shift?
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- The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 4 mm and a standard deviation of 0.03 mm. Suppose that the process will be monitored by selecting a random sample of 25 drives from each shift's production and determining x, the mean coating thickness for the sample. USE SALT (a) Describe the sampling distribution of x for a random sample of size 25. The distribution of x is ---Select-- ✓with mean 4- 20x = 4 + 20 = (b) When no unusual circumstances are present, we expect x to be within 20 of 4 mm, the desired value. An x value farther from 4 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 4 ± 20x mm mm and standard deviation mm mm. (c) Referring to part (b), what is the probability that a sample mean will be outside 4 ± 20 just by chance (that is, when there…The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determining x, the mean coating thickness for the sample. USE SALT (a) Describe the sampling distribution of x for a random sample of size 16. The distribution of X is ---Select--- ✓with mean mm and standard deviation mm mm mm. (b) When no unusual circumstances are present, we expect x to be within 20 of 3 mm, the desired value. An x value farther from 3 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 3 ± 20%. 3 - 20- 3 + 20 = (c) Referring to part (b), what is the probability that a sample mean will be outside 3 ± 20-just by chance (that is, when there…The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 5 mm and a standard deviation of 0.03 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determining x, the mean coating thickness for the sample. USE SALT (a) Describe the sampling distribution of x for a random sample of size 16. The distribution of x is ---Select--- ✓with mean 5 - 20 = 5 + 20x = mm and standard deviation (b) When no unusual circumstances are present, we expect x to be within 20 of 5 mm, the desired value. An x value farther from 5 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 5 ± 20%. mm mm mm. (c) Referring to part (b), what is the probability that a sample mean will be outside 5 ± 20 just by chance (that is, when…
- Forced expiratory volume (FEV) is an index of pulmonaryfunction that measures the volume of air expelled after 1second of constant effort. FEV is influenced by age, sex,and cigarette smoking. Assume that in 45- to 54-year-oldnonsmoking men FEV is normally distributed with mean =4.0 L and standard deviation = 0.5 L. In comparably aged currently smoking men FEV is nor-mally distributed, with mean = 3.5 L and standard deviation = 0.6 L. If an FEV of less than 2.5 L is regarded as showingsome functional impairment (occasional breathlessness,inability to climb stairs, etc.), then what is the probabilitythat a currently smoking man has functional impairment?Suppose a variable is Normally distributed with μ=345 and \sigma σ=30. What proportion of the data has values above 390? Use four decimal places in your answer.the life span of computer manufactured by xyz company is normally distributed with mean 8 years and standard deviation 1.5 years. what percentage of xyz monitors will remain operational after 9 years?
- Your hypothesis test for a mean with n = 18 has a two-tailed critical region. The test statistic is tt = -1.38. Find the p-value accurate to 2 decimal places.Citrus F v is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage uver the years for Citrus cars has been about 1600 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 21 recent mileages of Citrus cars was taken. The mean of these 21 mileages was 1553 miles per month, and the standard deviation was 241 miles per month. Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.05 level of significance, can it be concluded that the mean recent monthly mileage, u, of Citrus cars is less than 1600 miles per month? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null…Find the distribution of W = X^2 when X is Normally distributed with mean = 0 and variance = 4
- Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of m= 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of xbar= 7.2 ppb arsenic, with s= 1.9 ppb. Does this info indicate that the mean level of arsenic in this well is less than 8ppb? Use a= 0.01. Show full detail.The time that it takes a driver to react to the brake lights on a decelerating vehicle is critical in helping to avoid rear end collisions. A study found that the reaction time for an in traffic reponse to a brake signal from standard brake lights can be modeled with a normal distribution with a mean of 1.25 secs and standard deviation of 0.45 sec what percent of drivers have a reaction time between 0.35 sec and 2.80 ?In a manufacturing industry, the amounts which go into raw materials(scraps) are supposed to be normally distributed with mean GHC 36 and standard deviation GHC 0.1. Once every 30 minutes a scrap is selected from the production line, and it's contents are noted precisely. If the amount of scrap goes below GHC 35.8 or above GHC 36.2, then the scrap will be declared out of control. If the process shifts so that mean = GHC 37 and standard deviation of GHC 0.4, find the probability that a scrap will be declared out of control.