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.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2