The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches. A sample of 36 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.82 and 30.27 inches long?

nnEssay type Questions (10 points each)( You must show all your relevant work in Essay type to receive full points)nChapter 8n1. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.24 ounces. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have an average weight less than 15.97 ounces?nn2. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches. A sample of 36 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.82 and 30.27 inches long?nnChapter 9n3. The quality control manager of a tire company wishes to estimate the tensile strength of a standard size of rubber used to make a class of radial tires. A random sample of 49 pieces of rubber from different production batches is subjected to a stress test. The test measures the force needed to break the rubber in pounds. According to the sample results, the average pressure is 250 pounds and the standard deviation is 42 pounds. Determine the 95% confidence interval.nn4. The production manager for the XYZ manufacturing company is concerned that the customer orders are being shipped late. He asked one of his planners to check the timeliness of shipments for 900 orders. The planner randomly selected 900 orders and found that 180 orders were shipped late. Construct the 95% confidence interval for the proportion of orders shipped late.nn5. A cable TV company wants to estimate the percentage of cable boxes in use during an evening hour. An approximation based on previous surveys is 25 percent. The company wants the new estimate to be at the 90 percent confidence level and within 2 percent of the actual proportion. What sample size is needed?nnChapter 10n6. Given sample data: 61.2, 61.9, 62.8, 63.1, 64.0, 64.3, 64.9, 65.5, 66.3 and 67.9,ntest H0: m £ 62.89 versus H1: m > 62.89 at a = 0.05.nn7. Test H0: π = 0.25 versus HA: π ¹ 0.25 with p = 0.33 and n = 100 at alpha = 0.05 and 0.10.nn8. Test at α =.05 and 0.10 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 265 favor the system?nnChapter 13n9. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model.n∑X = 50n∑X2 = 200n∑Y = 75n∑Y2 = 1600n∑XY = 400nnFind the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination.Test the significance of the slope.nn10. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):n

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Brand	Price (X)	Score (Y)
Dell	3800	50
Hisense	2800	45
Hitachi	2700	35
JVC	3000	40
LG	3500	45
Maxent	2000	28
Panasonic	4000	57
Phillips	3200	48
Proview	2000	22
Samsung	3000	30

nUse the above data to develop and estimated regression equation. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3600 and perform significance test for the slope.nn