Consider a sample with a mean of 60 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number). a. 50 to 70, at least %
b. 35 to 85, at least %
c. 51 to 69, at least %
d. 47 to 73, at least %
e. 43 to 77, at least %

a)75%

b)96%

c)69.4%

d)85.2%

e)91.3%

Step by step explanation:

Given:

Mean=60

Standard deviation= 5

We were told to use chebyshev's theorem.to determine the percentage of the above given data within each of the following ranges

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is