A sample of 6 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 2.88,2.91,2.97,2.97,2.92,2.87

Standard deviation = 0.039 mm

Step-by-step explanation:

The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.

Mathematically,

Standard deviation = σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean

N = number of variables = 6

We first calculate the mean

xbar = (Σx)/N

xbar = (2.88+2.91+2.97+2.97+2.92+2.87)/6

xbar = (17.52/6) = 2.92 mm

Σ(x - xbar)² = [(2.88 - 2.92) + (2.91 - 2.92)² + (2.97 - 2.92)² + (2.97 - 2.92)² + (2.92 - 2.92)² + (2.87 - 2.92)²] = 0.0092

σ = √[Σ(x - xbar)²/N] = √(0.0092/6) = √0.0015333

σ = 0.039 mm

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

well

44-3-3-3=35

35+4+4+4+4=51

so the ansewr would be 51 degreesat 7: 00