Question

9. A large candy manufacturer produces, packages and sells packs of candy targeted to weigh 52 grams. A quality control manager working for the company was concerned that the variation in the actual weights of the targeted 52-gram packs was larger than acceptable That is, he was concerned that some packs weighed significantly less than 52-grams and some weighed significantly more than 52 grams. In an attempt to estimate o, the standard deviation of the weights of all of the 52-gram packs the manufacturer makes, he took a random sample ofn = 10 packs off of the factory line. The random sample yielded a sample variance of 4.2 grams. Use the random sample to derive a 95% confidence interval for a. 10. In a typical car, bell housings are bolted to crankcase castings by means of a series of 13 mm bolts. A random sample of 12 bolt-hole diameters is checked as part of a quality control process and found to have a variance of 0.0013 mm2 (a) Construct the 95% confidence interval for the variance of the holes. (b) Find the 95% confidence interval for the standard deviation of the holes. State clearly any assumptions you make. 11. Measurements are made on the lengths, in mm, of a sample of twenty wooden components for self-assembly furniture. Assume that these may be regarded as twenty independent observations from a normal distribution with unknown mean u and unknown variance o The data are as follows. 581 580 581 577 580 581 577 579 579 578 582 579 582 581 582 580 577 578 583 581 Find a 95% confidence interval for the variance a2 and hence find a 95% confidence interval for the standard deviation o

Answer 1

Seluition Here n=10 Sarmple vaiame u-2 At 95Y-/ lp 19.023 2-7 The 95y. c- I fo (n-D 9 u.2 9(4-2 27 2-7 19.023 2 .u0 96 L rL 3-第7U2_ hert WO.0013 zt3N2) n=1I2113P aん The 95% h s At 95%ノ ズーニ 3-816 -21-92/ -D n-DAZ o.0013) 211(0-0013) 3.86 .00065 LO00375 .2 21 92 う the 95y f8 C-ユ -00255 -ト 0.06122

hare trom the gven data Mニ20 よf= 20-1 -19 S3579/ At 95%, ニ32-852 A 8-907 95%. し The 19(3-579 19 (3-579 8-907 32-852 ニ 2-072 L7.63u6 The 9sy. f M-DR J2-07 ーム)7-63u6 Rale G = 1.439 4 2. 2763