14. use the given degree of confidence and sample data to construct a confidence interval for the population mean. assume that the population has a normal distribution.
n=10, x=8.7, s=3.3, 95% confidence
i know the answer is 6.34< μ< 11.06 but i dont know how to get there

Step-by-step explanation:

Confidence interval = mean ± margin of error

CI = μ ± ME

The mean is μ = 8.7.

Margin of error = critical value × standard error

ME = CV × SE

At 95% confidence and 9 degrees of freedom, CV = 2.262.

SE = s / √n

SE = 3.3 / √10

SE = 1.04

The margin of error is:

ME = 2.262 × 1.04

ME = 2.36

CI = 8.7 ± 2.36

CI = (6.34, 11.06)

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice