1. [45 pts.] As part of its quality-control program, an aspirin manufacturer measures the dosage of the active ingredient, salicylic acid, in its pills. A sample of 27 pills yields the following data, which has been sorted. Assuming the population of pill dosages is Gaussian, Salicylic a. [10 pts - 5 min] Test for mild and extreme outliers ONLY ON THE HIGH acid per END of the data (there are none on the low side), and identify them. (Do not pill, X discard them for the questions that follow.) No (mg) (x - x)' 324.1 123.79 b. [20 pts -10 min] Pharmacological standards require that at each pill contain 325 324.4 117.20 mg or more. Can we expect that 98% of the population of pills has a dosage 325.8 88.85 greater than 325 mg? 326.9 69.32 328.6 43.90 c. [15 pts -10 min] The usual dosage is two pills. Predict the dosage one would 329.6 31.65 receive by taking two pills (assume 98% confidence). 331.1 17.02 331.5 13.88 331.7 12.43 332.2 9.16 11 333.0 4.95 12 333.1 4.52 13 333.2 4.10 14 333.4 3.33 15 333.8 2.03 16 334.1 1.27 17 335.7 0.22 18 336.2 0.95 19 339.3 16.60 20 340.5 27.82 21 341.0 33.34 22 341.4 38.12 23 341.7 41.91 24 343.3 65.19 25 343.7 71.81 26 344.9 93.59 27 356.9 469.77 sums 9051.1 1406.73