Math 370 HW 3 - Homework3 3-43, 3-44, 3-50, 3-57, 3-62,...

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1Homework33-43, 3-44, 3-50, 3-57, 3-62, 3-633-43.a) P(X < 31) = P(Z < -3) = 0.001350b) P(X > 30) = P(Z > -3.5) = 0.999767c) P(33 < X < 37) = P(-2 < Z < 0) = P(Z < 0)P(Z < -2) = 0.50.02275 = 0.47725d) P(32 < X < 39) = P(-2.5 < Z < 1) = 0.8413450.00621 = 0.835135e) P(30 < X < 38) = P(-3.5 < Z < 0.5) = 0.6914620.000233 = 0.6912293-44.a) P(X > x) = 1P(X < x)= 1 -36xZP= 0.50.And,36xZP= 0.50Therefore,36x= 0 and x = 6.b) P(X > x) = 1P(X < x)= 1 -36xZP= 0.95.And,36xZP= 0.05Therefore,36x= -1.645 and x = 1.065.c) P(x < X < 9) = 0.20641345.036xZP20.0841345.036xZP20.036xZP841345.020.036xZP)1Z(P1Z36xP369Z36xP
2Therefore,36x=0.36, and x = 7.08.d) P(3 < X < x) = 0.80PZxPZxP ZxP ZP ZxP Zx36363163631080630158655080630 958655

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