Arandom sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16. (give answers to four decimal places.) a) give the mean and standard deviation of the (repeated) sampling distribution of x. mean = standard deviation = b) calculate the standard normal z-score corresponding to a value of x = 16. c) calculate the standard normal z-score corresponding to a value of x = 23. d) find p(x < 16). e) find p(x > 23). f) find p(16 < x < 23).

(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

its a straight line parallel to the time axis

irrational, cannot