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

In this assignment we will discuss about mathematical problems and below are the summaries point:- Given a function f(x) = ax4-bx2, find the critical points, and greatest absolute value of f(x). Evaluate the integral of a function within given boundaries. Solve an equation with a variable exponent and find the value of a constant. Evaluate the value of a constant in a given equation. Find the value of q that satisfies the derivative of a given function. Evaluate the integral of a given function within given boundaries. Solve an integral equation and find the value of an unknown constant. Solve an integral equation and find the value of an unknown constant. Solve a system of equations with two unknowns and evaluate the value of an expression. Solve an equation and find the value of a constant.

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

Statistics 4
5x2 =q
Q = 281.25
Question 6
∫
a
b
x ❑c+d
x dx
= ∫
a
b
❑ xc/x + d/x dx
= ∫
a
b
❑ xc+1/x (c+1) + d2/2x dx
But a=2.4, b=10.5, c=2 and d=30
= x3/3x + 90/2x
= 10.53/(10.5) + 90/2(10.5) – 10.52.4/3(2.4) + 90/2(2.4)
= 36.75 + 4.286 – 39.22 + 18.75
= 41.036 – 57.97
= -16.93
Question 7
∫
❑
❑ ax +b
x ❑2 −9 x+20 dx
= ax2/2 +bx+c – x3/3-9x2/2+20x +c
= 10x2+4.5x2-69x-20x-x3/3
=14.5x2-89x-3lnx3+c
=14.50
Question 8
∫
❑
❑ ax +b
x ❑2 +5 x−14 dx
ax ❑2
2 +bx+c
x 3
3 + 5 x 2
2 −14 x +c
dx
=38.5x2+bx+c-(3lnx3-2.5x2-14x+c)
=41x2+bx+14x-3lnx

Statistics 5
= 41
Question 9
Y=ax2-bx
Y = cx-dx2
ax2-bx=cx-dx2
ax2+dx2=cx-bx
= x2(a+d)=x(c-b)
=137.8x2=-18.8x
=x(137.8x-18.8)=0
X=0 0r x=137.8/18.8
=-7.33
A= ∫
−7.33
0
( x−dx 2 )−(ax 2−bx)
= -7.332/2 – 84.3 (-7.33)3/3- 53.5 (-7.33)3 – 54.8 (-7.33)2/2
= 26.86 + 11066.70
= 19,589.08
Area = 0-19,589.08
=-19,589.08 square units
Question 10
a= Vf-Vi/t
v= D/T
48 = 344m/t
T = 7.17 seconds
a= 48/7.17
= 6.60 m/s
Question 11
In a 3 fair dice there are 6x6x6 =216 possible outcomes
Chances of appearing on 1st die = 1/6
There are six ways to get 555 only

Statistics 6
Hence, 6/216
=0.03
Question 12
P(1 tripple) = 11/36
But 400 rolls
=1/36 x 400
=11.1111
Question 13
P(choosing an integer between 1 and 56) = 1/56
Possible outcomes = 112
P(only 2 men choose same) =56/112
=0.500
Question 14
Probability of choosing same number = 1/49
P(choosing different number) = 1-1/49
5 people = 1-1/49*5
=4.8979
Question 15
Possible outcomes 25 = 32
P(all outcomes same) = 1/16
P(not same) = 1-1/16 = 15/16
=0.9375
Question 16

Statistics 7
x x-xbar
x-xbar
sqrd
16 -10.2857 105.7959
11 -15.2857 233.6531
23 -3.28571 10.79592
29
2.71428
6 7.367347
44
17.7142
9 313.7959
34
7.71428
6 59.5102
27
0.71428
6 0.510204
184 731.4286
26.2857
1
=√ 731.4286/7
= 11.04
Question 17
x f x-xbar
x-xbar
sqrd
f(x-xbar
sqrd)
18 13 -18 324 4212
38 29 2 4 116
52 36 16 256 9216
total 108 78 584 13544
mean 36
= √13544/78
=13.18
Question 18
Z values for CI of 95% = 1.96
= 31.71+- 1.96 *12.39/√71

Statistics 8
= 31.71 + 2.88 or 31.71- 2.88
Upper limit = 34.59
Question 19
Z values for 99% CI = 2.58
=21.04+- 2.58 *2.56/√307
= 21.04+- 0.37
Lower limit
=21.04-0.37
=20.66
Question 20
= 4.4+- 2.58 * 0.37/√1126
= 4.4 +- 0.03
Lower limit
= 4.37