Stats_Material49 - Q1 A To find P(a < Z < b = F(b F(a P(X <...

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Q1 A. To find P(a < Z < b) = F(b) - F(a) P(X < 0.03) = (0.03-0)/1 = 0.03/1 = 0.03 = P ( Z <0.03) From Standard Normal Table = 0.51197 P(X < 1.01) = (1.01-0)/1 = 1.01/1 = 1.01 = P ( Z <1.01) From Standard Normal Table = 0.84375 P(0.03 < X < 1.01) = 0.84375-0.51197 = 0.3318 OR 33.18% B. To find P(a < Z < b) = F(b) - F(a) P(X < 3) = (3-0)/1 = 3/1 = 3 = P ( Z <3) From Standard Normal Table = 0.99865 P(X < 4) = (4-0)/1 = 4/1 = 4 = P ( Z <4) From Standard Normal Table = 0.99997 P(3 < X < 4) = 0.99997-0.99865 = 0.0013 OR 0.13% Q2 Ans. Normal Distribution Mean ( u ) = 56.4 Standard Deviation ( sd )=4.8 Normal Distribution = Z= X- u / sd ~ N(0,1) To find P(a < Z < b) = F(b) - F(a) P(X < 46.5) = (46.5-56.4)/4.8 = -9.9/4.8 = -2.0625 = P ( Z <-2.0625) From Standard Normal Table = 0.01958 P(X < 65) = (65-56.4)/4.8 = 8.6/4.8 = 1.7917 = P ( Z <1.7917) From Standard Normal Table = 0.96341 P(46.5 < X < 65) = 0.96341-0.01958 = 0.9438 OR 94.38%
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Q3 Ans. A. From the table we know that it equals to 1.96 B. From the table we know that it equals to -1.96 Q4 A. Normal Distribution = Z= X- u / sd ~ N(0,1) P(0.975) = X – 56.4 / 4.8 & We know that P(0.975)=1.96 1.96 (4.8) = X – 56.4 X = 9.408 + 56.4 = 65.808 B. Normal Distribution = Z= X- u / sd ~ N(0,1) P(0.025) = X – 56.4 / 4.8 & We know that P(0.025)=-1.96 -1.96 (4.8) = X – 56.4 X = -9.408 + 56.4 = 46.992 Q5 Normal Distribution Mean ( u ) =56.4 Standard Deviation ( sd )=4.8 Normal Distribution = Z= X- u / sd ~ N(0,1)
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P ( Z > x ) = 0.95 Value of z to the cumulative probability of 0.95 from normal table is -1.64 P( x-u/ (s.d ) > x - 56.4/ (4.8 ) = 0.95
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