Arandom sample of 41 car owners results in a mean of 7
years. assume a population a standard deviation of 3.75 years. find
a 95 %confidence interval for the true population mean. identify
thepoint estimate for the mean and margin of error. using this
infofind a 95% confidence interval for the population variance
andstandard deviation. identify the point estimates for both.

Margin of error = ±1.96*std error

= ±1.1479

Confidence interval = Mean ±1.1479

=

Step-by-step explanation:

given that a random sample of 41 car owners results in a mean of 7

years.Assume a population a standard deviation of 3.75 years.

By central limit theorem we can say sample mean will have point estimate as 7 and std error as =

Since population std deviation is known and sample size >30 and also random is assured we can use Z critical value for finding out the margin of error.

95% Z critical value = ±1.96

Margin of error = ±1.96*std error

= ±1.1479

Confidence interval = Mean ±1.1479

=

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

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