Ten samples of coal from a Northern Appalachian source had an average mercury content of 0.242 ppm with a standard deviation of 0.04 ppm. Find a 95% confidence interval for the mean mercury content of coal from this source. Round the answers to four decimal places.

0.2172<x<0.2668

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as;

CI = xbar ± (z*s/√n)

xbar is the average = 0.242ppm

z is the z score at 95% confidence = 1.96.

s is the standard deviation = 0.04pm

n is the sample size = 10

substitute the values into the formula;

CI = xbar ± (z*s/√n)

CI = 0.242 ± (1.96*0.04/√10)

CI = 0.242 ± (1.96*(0.04/3.1623))

CI = 0.242 ± (1.96*(0.01265))

CI = 0.242 ± (0.02479)

CI = (0.242-0.02479, 0.242+0.02479)

CI = (0.2172, 0.2668)

Hence a 95% confidence interval for the mean mercury content of coal from this source is 0.2172<x<0.2668.

b

step-by-step explanation:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3