matma

uczelnia/2_semestr/matematyka_stosowana/laby/lab_5.R

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+# Zadanie 1
+A = matrix(c(1, 1, qnorm(0.3), qnorm(0.75)), 2, 2)
+B = c(5281.21, 9090.9)
+wynik = solve(A, B)
+m = wynik[1]
+sigma = wynik[2]
+print(m)
+print(sigma)
+
+# a)
+# P(x > 7800)
+pnorm(7800, m, sigma, F) * 100 # 39.42534
+
+# b)
+round(qnorm(15/100, m, sigma),2) # 3654.13
+
+# zadanie 2
+A = matrix(c(1, 1, qnorm(0.8), qnorm(0.44)), 2, 2)
+B = c(120, 90)
+wynik = solve(A, B)
+
+m = wynik[1]
+sigma = wynik[2]
+
+# a)
+# P(X < 45)
+pnorm(45, m, sigma) # 0.05051767
+
+# b)
+qnorm(0.13, m, sigma, F) # 128.6069
+
+# zadanie 3
+m = 165.5
+sig = (155 - m)/qnorm((1 - 0.93)/2)
+round(pnorm(170, m, sig, F) * 500)
+
+# zadanie 4
+A = matrix(c(1, 1, qnorm(11/12), qnorm(2/12)), 2, 2)
+B = c(0.9, 0.5)
+wynik = solve(A, B)
+m = wynik[1]
+sigma = wynik[2]
+
+qnorm(0.1, m, sig, F)
+
+# zadanie 5
+m = 4001.50
+sig = (3503 - m)/qnorm((1 - 0.15)/2)
+qnorm(0.25, m, sig, F)
+
+# zadanie 6
+# 45 < X < 55
+
+A = matrix(c(1, 1, qnorm(2/524), qnorm(517/524)), 2, 2)
+B = c(17, 70)
+wynik = solve(A,B)
+m = wynik[1]
+sig = wynik[2]
+
+pnorm(55, m, sig) - pnorm(45, m, sig)