A distribution of measurements has a mean of 65 and a standard deviation of 7. You know nothing else about the size or shape of the data. Use this information to find the proportion of measurements in the given interval. (Round your answer to two decimal places.) between 44 and 86

The proportion of measurements in the given interval is 88.89% .

Step-by-step explanation:

We are given that a distribution of measurements has a mean of 65 and a standard deviation of 7 i.e.;   = 65    and   = 7

Also, we know nothing about the size or shape of the data. So, here we will use the Tchebysheff's Theorem.

According to this theorem, the lower bound formula for any population data set is given by;

                  Lower bound =

On the other hand, upper bound formula for any population data set is given by;

                  Upper bound =

In the question we have to find the proportion of measurements in the given interval of 44 to 86 i.e. Lower bound = 44 and Upper bound = 86

Therefore,     44 =              and              86 =  

                     44 = 65 - k * 7             and              86 = 65 + k * 7

                      k = = 3                 and               k = = 3

Now, proportion of measurements in any given interval is given by;

                  P =

                  P = = = 88.89%

Therefore, the proportion of measurements in the given interval of between 44 and 86 is 88.89%.

(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

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: