II (No.1) 1 x 1, x 2,..., x µ = 1 V = 1 k=1 x k (x k µ) 2 k=1 σ = V. V = σ 2 = 1 x 2 k µ 2 k=1 1 µ, V σ. (1) 4, 7, 3, 1, 9, 6 (2) 14, 17, 13, 11, 19, 16 (3) 12, 21, 9, 3, 27, 18 (4) 27.2, 29.3, 29.1, 26.0, 27.2, 24.6, 30.2, 27.6, 25.6 2 3 79 74 82 32 25 17 3 50 52 42
II (No.2) 2 4,.. (1) (cm) (2) (cm) 155 160 5 155 160 63 160 165 18 160 165 51 165 170 42 165 170 45 170 175 27 170 175 60 175 180 8 175 180 81 5 36, (). 146.6 155.3 136.2 151.9 162.7 153.3 161.5 170.8 156.0 158.1 142.3 154.0 157.9 143.0 153.7 151.2 167.2 146.9 156.2 157.3 150.2 145.7 161.1 156.3 151.7 137.3 154.8 141.7 151.4 150.7 148.8 143.4 155.0 159.3 158.1 147.5 (1) 135g 5g. (2) (1),. (3),.
II (No.3) 3 X µ, σ 2, X N(µ, σ 2 )., Z 0, 1, Z. 6 Z. (1) 0 < Z < 1.96. (2) 2.58 < Z < 2.58. (3) Z > 1.64. (4) 1.34 < Z < 1.79. (5) Z < 1.04. (6) Z < 1.27. (7) 1.57 < Z < 2.46. (8) Z > 1.70. (9) 2.89 < Z < 1.53.
II X µ, σ 2, Z = X µ, Z σ., a < X < b, a µ < Z < b µ. σ σ 7 (No.4) 27 17 157.9cm, 5.38cm. (http://www.e-stat.go.jp/sg1/estat/newlist.do?tid=000001011648) (1) 17 162.5cm. (2) 17 150.0cm. (3) 17 155.0cm 160.0cm. 8 X N(µ, σ 2 ). (1) µ σ 2 < X < µ + σ 2. (2) µ + 0.5σ < X < µ + 1.5σ. (3) X > µ + 1.5σ. 9 S K 80.3, 5.7., T K 58.1, 10.3. S A 88, T B 75., A B,. X N(µ, σ 2 ) Z = X µ σ Z N(0, 1)
II (No.5) 4 X 1, X 2,..., X, X = X 1 + + X S 2 = (X 1 X) 2 + + (X X) 2 U 2 = (X 1 X) 2 + + (X X) 2 1 = X2 1 + + X 2 ( X) 2 µ, σ 2, N σ, X 2 µ,. S 2 1 σ2 U 2 σ 2. N, X µ, N 1 σ2. S 2 N N 1 1 σ2 U 2 N N 1 σ2. σ 2 ( ) σ 2, S 2 U 2. 10 4 1, 3, 9, 11 4. 2.. (1) µ, σ 2. (2) X,. (3) S 2 11 (1) X,. (2) S 2 U 2.. 12 2000 22.4g, 4.8g, 36. (1), (2),,,,. 72.
II (No.6) 5 (, ),. µ, σ 2, X µ, σ2. 13 8.00mm, 0.80mm. 16 (1) 7.90mm 8.10mm (2) 8.20mm (3) 7.70mm. 14 64. 15, 30kg 5kg. 780kg, 25. 24. X N ( µ, σ2 )
II (No.7) 6 6.1 ( ), 16 100, 5.7. 95%. 16 40 250, 824. 90%. 17 100. 99% ±20,. X µ σ/ N(0, 1)
II (No.8) 6.2 ( ) µ, X, X µ U, U/ 1 t. t N(0, 1). 18 15, 4.4g/dl, 0.59g/dl. 90%. 19 9,. ( mm) 27.2, 29.3, 29.1, 26.0, 27.2, 24.6, 30.2, 27.6, 25.6 95%. 20. 120, 58.3, 12.4. 90%. X µ U/ t 1 > 30 X µ U/ N(0, 1)
II (No.9) 6.3 σ 2, U 2, ( 1)U 2 1 χ 2. σ 2 21 10 1.20mm. 90%. 22 A 14,. 96, 94, 107, 101, 98, 98, 104, 99, 95, 100, 102, 98, 96, 98 A 98%. ( 1)U 2 χ 2 1 σ 2
II (No.10) 6.4 p P p, p(1 p). 23, 600. 10% 90%. 24 2000,, 762. 99%. P p p(1 p) N(0, 1)
II (No.11) 7 ( ) 10, 6, 4. p. 25 { λe λx, 0 x, f(x) = 0, (λ > 0). X 1, X 2,..., X, λ. 26 µ V V X 1,..., X, µ. 27 µ V µ X 1,, X, V. N(µ, V ) f(x) = 1 2πV e (x µ)2 /2V.
II (No.12) 8 5, 16, 100, 5.7. (1), 5%. (2), 5%. 28 1500,, 120, 1470, 125., 1%. 29 13.0km/l., 5, 10.7km/l, 2.1km/l.,,,, 1%. 30 45%.,, 80 42.. 5%. 31 0.41mm.,, 12 0.60mm., 5%.
II (No.13) 9 χ 2 9.1 k C 1,..., C k, C 1 C 2 C k () m 1,..., m k. f 1 f 2 f k, C 1,..., C k m 1 m 2 m k () f 1,..., f k, T = (f 1 m 1 ) 2 + + (f k m k ) 2 m 1 m k k 1 χ 2. 32, 300. ( 1/6 ), 5%. 1 2 3 4 5 6 60 41 57 38 62 42 300 33 A : B : O : AB = 4 : 2 : 3 : 1. 150,., 1%. A B O AB 78 24 36 12 150 9.2 34, 30,., 5%. 115 62 90 33 300 38 80 56 26 200 153 142 146 59 500 35 200,. (1). (2).,, 1%. (2) (1) 75 45 120 45 35 80 120 80 200