The owner of a manufacturing plant employs eighty people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The distances for a random sample of six employees are listed below: 26 32 29 16 45 19

Required:
Compute mean, variance, and standard deviation for these data, with a step-by-step explanation for each. Round your answer to one more decimal place than the original data.

Mean of the sample = 27.83

The variance of the the sample = 106.96

Standard deviation of the sample = 10.34

Step-by-step explanation:

Step(i):-

Given random sample of six employees

x     26    32    29    16     45    19

mean of the sample

Mean of the given data = 27.83

Step(ii):-

Given data

x           :       26         32           29           16           45        19

x - x⁻     :      -1.83      4.17        1.17       -11.83     17.17    -8.83

(x - x⁻)²  :    3.3489   17.3889   1.3689   139.9489  294.80 77.9689

∑ (x-x⁻)²  =   534.8245

Given sample size 'n' =6

The variance of given data

           S²  = ∑(x-x⁻)² / n-1  

The variance of the given sample = 106.9649

Step(iii):-

Standard deviation of the given data

Standard deviation of the sample = 10.3423

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

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step-by-step explanation: