STAT 571 Midterm: STAT 571 UW Madison Fall 00Mid1 Solutions
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1. (a) the stem and leaf display is useful for a small data set such as this. (b) v ar(y ) = 0. 80 (0 2. 18)2+0. 18 (1 2. 18)2+ 0. 02 (100 2. 18)2 = 195. 42 = 13. 972. Yna n (2. 18, 195. 42/100) by the central limit theorem (clt) and p ( y 2) p ( yna : = p (z 2 2. 18. 1. 397 ) = p (z 0. 129) = The display appears roughly symmetrical, cen- tered around 6. 7. Median y[0. 50] = 6. 75. (b) since y n (6. 45, 0. 30/15), p ( y < 6. 60) = ) = p (z < 1. 06) = 0. 8554. 4. (a) p (y1 7) = p (y1 = 7) + p (y1 = 8) = 0. 2552. (b) p (y2 7) = p (z 7 5. 6. ) = p (z 1. 08) = (c) e(y1) = 8 0. 7 = 5. 6 = e(y2) and v ar(y1) =
