| Jumat, 27 November 2009 |
| My Assignment about problems of mathematics |
1. draw a contour curve z=k for values of k which given.
z= 1/2 (x^2+y^2 ) , k = 0,2,4,6,8.
2. showed that surface x^2+4y+z^2=0 and x^2+y^2+z^2-6z+7=0 each other touching in point (0, -1, 2), showing that they have same area in point (0, -1, 2)
3. calculate the area under 32 if given a normal distribution with µ = 40 and σ = 6.
4. calculate the value of x which the area under 45% with µ = 40 and σ = 6.
5. given a randow sample which have measure 24 which pulled by a normal population. calculate k if P (-2.069 < T < k)= 0.965.
SOLUTION:
1. 
2. F(x,y,z) x^2+y^2+z^2-6z+7=0
<=> Fx (x,y,z) = 2x --> Fx (0,-1,2) = 0
<=> Fy (x,y,z) = 2y --> Fy (0,-1,2) = -2
<=> Fz (x,y,z) = 2z-6 --> Fz (0,-1,2) = -2
so, the surface area y+z-1=0
F(x,y,z) x^2+4y+z^2=0
<=> Fx (x,y,z) = 2x --> Fx (0,-1,2) = 0
<=> Fy (x,y,z) = 4 --> Fy (0,-1,2) = 4
<=> Fz (x,y,z) = 2z --> Fz (0,-1,2) = 4
so, the surface area y+z-1=0
because the both of surface area is same, so the surface is proven that they have same area.
3. z = (x-µ)/σ = -4/3
P (X < 32) = P (Z < -4/3)
= 0.0918
so, the answer is 0.0918.
4. P(X < x) = 45% = 0,45
z which have value 0.45 is -0.13
z = (x-µ)/σ
(-0.13)(6) = x-40
x = 39.22
so, the value of x is 39.22
5. P (-2.069 < T < k)= 0.965
-2.069 = t(-0.025)
<=> 1 - k - 0.025 = 0.965
<=> k = 0.010
t(k)=t(0.010)= 2.500
so, the value of k is 2.500 |
posted by sOFFia aNisa H.A.C (08305141004) @ 22.03  |
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