A random sample of 8 recent college graduates found that starting salaries for computer scientists had a mean of $85000 and a standard deviation of $15000. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all computer scientists in gainesville.

(72460, 97540)

Step-by-step explanation:

Given:-

- The sample size, n = 8

- The sample parameters of normal distributed data:

                     mean u = $85000

                     standard deviation s.d = $15000

Find:-

Construct a 95% confidence interval for the average starting salary of all computer scientists in gainesville.

Solution:-

- A random variable (X) denotes average starting salary of all computer scientists in gainesville has a sample normally distribution as follows:

                              X ~ N ( $85000 , $15000^2 )

- The general formulation for CI for known standard deviation with significance α = 1 - 0.95 = 0.05:

                    ( u - Z_a/2*(s.d/√n) < X < u + Z_a/2*(s.d/√n) )

- The Z_a/2 = Z_0.025 = 1.96:

                    ( 85,000 - 1.96*(15,000/√8) < X < 85,000 + 1.96*(15,000/√8) )

                    (72460, 97540)

(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