Question

Problem 3: From a production run of 10,000 helical gears, a sample of 20 are randomly selected and tested to determine if the surface hardness Jneets the required specifications. The Brinell hardness value for each of the gears is provided in the files tab of the class Canvas website labeled HW 8 Data.xlsx' on the second sheet of the workbook. Calculate the sample mean and sample standard deviation of the data. Using these values, determine the range within which the mean of the entire population of 10,000 gears exists with probabilities of 95% and 99%. Additionally, find the range of hardness values that would provide a 95% probability that if a gear was selected at random from the entire population, the tested Brinell hardness for this part would exist within the stated range.

Answer 1

Uploading the answers.

First of all I've calculated the sample mean and sample standard deviation. Take a look:-
432.52 CAns ) enlev above 2 (1-12 x sample dala po do oints are for拘 S e. daea Polat above 432.52 432.52

Sandan (A 35, 6-932, 52) t(у 35,6-니32.52) 刃 + (15)-9 32 2 15 4 43.5 2) 2.5) 2. 3.5 2) ./소65.7829 12.9756
uploading answer for the last part:-

so Range of the Brinell Hardness is 407.28 - 457.75.

のしJ that, es ,ケ つブ..phe Dhabiじん ,ち え n -9、32-52 12.835b Bri? en aches sts Minimum 12 8756 ウTme2て407.28