An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, and 50.06. Calculate the sample mean and sample standard deviation.

Mean = 43.969

Standard deviation = 12.341

Step-by-step explanation:

Given the data :

36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, 50.06

The sample mean :

Σx / n = 351.75 / 8 = 43.969

Sample standard deviation :

√Σ(x - mean)²/n-1

√[(36.45-43.969)² + (67.90-43.969)² + (38.77-43.969)² + (42.18-43.969)² + (26.72-43.969)² + (50.77-43.969)² + (38.9-43.969)² + (50.06-43.969)² ] / ((8 - 1)

Standard deviation = 12.341

there is no points to select.

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.