10 Statistical Calculations and Solutions for Practice - A Comprehensive Guide for Students

Running head: Statistics 1
Statistics
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Statistics 2
Question 1
F(x) = ax4-bx2
F’(x) = 4ax3-2bx
F’(x) =0 = 4ax3 -2bx
X (2ax2-b) = 0
X = 0
2ax2 = b
But a =67.5, b = 54.4
135x2 = 54.4
X2 = 0.40
X = 0.63
F(0) = 0
F(0.63) = 67.5 (0.63)4 – 54.4 (0.63)2
= 10.63 – 21.59
= -10.96
Critical points = (0, 0) (0.63, -10.96)
Greatest absolute value = 0
Question 2
Boundaries (86, 86.2)
Nax(n/m)-1 + -kbx-k-11
= 16x - 372x-7
=16(86.2) – 372(86.2)-7 – 16(86) – 372 (86)-7
= 1379.2- 1376
= 3.2
Question 3
F(x) = a/xb
F(x) = a.x-b
F’(x) = -bax-b-1
F’’(x) = b2+baxb+1

Statistics 3
But a=23, b=89
89(90+1)23x89+1
= 8010.23x90
= 184,230x90
c-d = 184,140
Question 4
∫
1
3
f ( x ) dx−kxdx = a
∫
1
3
b−kxdx =13
∫
1
3
7−kxdx =13
∫
1
3
−6=k ∫ xdx
-6x = kx2/2
-18 = 4.5k
K=-4
-6 = 0.5k
K =-12
-4+12 = 8
K =8
Question 5
Dy/dx = 2x +q/5x2
Gradient at turning point, derivative =0
2x +q/5x2 =0
= 5x2 – q = 0