zreczc

uczelnia/2_semestr/matematyka_stosowana/laby/lab_4.R

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+# zadanie 1
+
+# a)
+# P(x > 5) = 70 / 200
+x_5 = 70 / 200
+# P(x <= 5) = 1 - x_5
+x_5_F = 1 - x_5
+sigma = 1
+# (5 - m) / sig = qnorm(1 - 70/200)
+m = 5 - sigma * qnorm(x_5_F)
+
+round(pnorm(6, m, sigma) - pnorm(3, m, sigma), 4) # 0.8638
+
+# b)
+# P(x < 6) = 0.8
+x_6 = 0.8
+wariancja = 4
+sigma = sqrt(wariancja) # 2
+# (6 - m) / sigma = qnorm(0.8)
+m = 6 - qnorm(0.8) * sigma
+round(pnorm(6, m, sigma) - pnorm(3, m , sigma), 4) # 0.5449
+
+# zadanie 2
+m = 5.2 # w procentach
+
+# P(x < 3) = 12.1%
+P_x = 0.121
+# (3 - m) / sigma = qnorm(P_x)
+sigma = (3 - m)/qnorm(P_x)
+print(sigma) # 1.880338
+
+qnorm(0.8, m, sigma) # 6.782532%
+
+# zadanie 3
+m = -5
+# P( X < -2) = 0.95
+sig = (-2 - m)/qnorm(0.95)
+sig # 4.255698
+# P(X > 0)
+pnorm(0, m, sig, F) # 0.003058688
+
+# zadanie 4
+# aby zdać: ponad 50%
+# pierwszy termin: średnio: 46%, zdawalność: 40%
+
+# a)
+# P(X > 0.7) = ?
+a = 0.7
+m = 0.46
+sigma = (0.5 - m)/qnorm(0.6)
+pnorm(0.7, m, sigma, F)
+# b)
+qnorm(0.1, m, sigma, F)
+
+
+# zadanie 5
+sigma = 0.12
+# P(x > 0.8) = 3/12
+P_x = 3/12
+# (0.8 - m) / sigma = qnorm(3/12)
+m = 0.8 - qnorm(1 - P_x) * sigma
+qnorm(0.1, m, sigma, F) # 0.8728474
+
+# zadanie 6
+m = 86.5
+P_x = 0.3472
+a = 82.5
+
+sigma = (a - m)/qnorm((1 - P_x)/2)
+round(pnorm(95, m, sigma, F) * 400) # 68
+
+
+
+