Question #262396

The following data give the percentage of criminals for different age groups:

Age (less than X) 25 30 40 50 55 65

% of criminals 52 67.3 84.1 94.4 104.7 M


In the above table the value of M depends on Student ID. Suppose, one student ID

is 1503001, then the value of M would be: 001+100 meaning that last 3digits of

student ID+100. If anyone ID is 1503101 then the value of M would be: 101+100. The

value of M should be considered last 3 digits of student ID+100 and proceed

successively.

Using Lagrange’s formula, find the percentage of criminals under the age of 45.


1
Expert's answer
2021-12-07T10:34:30-0500

f(x)=(xx1)(xx2)(xx3)(xx4)(xx5)(x0x1)(x0x2)(x0x3)(x0x4)(x0x5)y0+(xx0)(xx2)(xx3)(xx4)(xx5)(x1x0)(x1x2)(x1x3)(x1x4)(x1x5)y1+(xx0)(xx1)(xx3)(xx4)(xx5)(x2x0)(x2x1)(x2x3)(x2x4)(x2x5)y2+(xx0)(xx1)(xx2)(xx4)(xx5)(x3x0)(x3x1)(x3x2)(xx4)(xx5)y3+(xx0)(xx1)(xx2)(xx3)(xx5)(x4x0)(x4x1)(x4x2)(x4x3)(x4x5)y4f(x)= \frac{(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5)}{(x_0-x_1)(x_0-x_2)(x_0-x_3)(x_0-x_4)(x_0-x_5)}y_0+ \frac{(x-x_0)(x-x_2)(x-x_3)(x-x_4)(x-x_5)}{(x_1-x_0)(x_1-x_2)(x_1-x_3)(x_1-x_4)(x_1-x_5)} y_1+ \frac{(x-x_0)(x-x_1)(x-x_3)(x-x_4)(x-x_5)}{(x_2-x_0)(x_2-x_1)(x_2-x_3)(x_2-x_4)(x_2-x_5)}y_2+ \frac{(x-x_0)(x-x_1)(x-x_2)(x-x_4)(x-x_5)}{(x_3-x_0)(x_3-x_1)(x_3-x_2)(x-x_4)(x-x_5)} y_3+ \frac{(x-x_0)(x-x_1)(x-x_2)(x-x_3)(x-x_5)}{(x_4-x_0)(x_4-x_1)(x_4-x_2)(x_4-x_3)(x_4-x_5)} y_4


f(x)=(4530)(4540)(4550)(4555)(4565)(2530)(2540)(2550)(2555)(2565)52+(4525)(4540)(4550)(4555)(4565)(3025)(3040)(3050)(3055)(3065)67.3+(4525)(4530)(4550)(4555)(4565)(4025)(4030)(4050)(4055)(4065)84.1+(4525)(4530)(4540)(4555)(4565)(5025)(5030)(5040)(5055)(5065)94.4+(4525)(4530)(4540)(4550)(4565)(5525)(5530)(5540)(5550)(5565)104.7f(x)= \frac{(45-30)(45-40)(45-50)(45-55)(45-65)}{(25-30)(25-40)(25-50)(25-55)(25-65)}52+ \frac{(45-25)(45-40)(45-50)(45-55)(45-65)}{(30-25)(30-40)(30-50)(30-55)(30-65)} 67.3+ \frac{(45-25)(45-30)(45-50)(45-55)(45-65)}{(40-25)(40-30)(40-50)(40-55)(40-65)}84.1+ \frac{(45-25)(45-30)(45-40)(45-55)(45-65)}{(50-25)(50-30)(50-40)(50-55)(50-65)} 94.4+ \frac{(45-25)(45-30)(45-40)(45-50)(45-65)}{(55-25)(55-30)(55-40)(55-50)(55-65)}104.7


=1305243567.3+81584.1+4594.4415104.7=\frac{1}{30}\cdot52 -\frac{4}{35}\cdot67.3 +\frac{8}{15}\cdot84.1 + \frac{4}{5}\cdot94.4 -\frac{4}{15}\cdot104.7


=86.5%=86.5\%



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