SOLUTION: Chebychev's Theorem: Suppose the time needed to assemble a piece of furniture is not normally distributed and that the mean assembly time is 28 minutes. What is the value of the s

The mean is 28 minutes.  Therefore

24 minutes is 4 minutes below the mean and 32 minutes is 4 minutes
above the mean,  So we are talking about 4 minutes from the mean.
We want to know what standard deviation would guarantee that at least
77% of the data would lie within 4 minutes of the mean.

Chebychev's theorem says that 100(1-)% of the data lies within
k standard deviations of the mean.  That means that ks = 4, where s is 
the standard deviation.

So first find k by setting 100(1-)% equal to 77% and solve 
for k:

100(1-)% = 77%

Drop the percents:

100(1-) = 77

Divide both sides by 100

1 -  = .77    <--(If your book just gives 1- you can start here)

Clear of fractions by multiplying through by k²:

         k² - 1 = .77k²

Get the k² terms on the left and the 1 on the right:

     k² - .77k² = 1

Factor out k² on the left:

    k²(1 - .77) = 1

        k²(.23) = 1

Divide both sides by .23

             k² = 

             k² = 4.347826087

Take the square root of both sides:

              k = 2.085144141

So that means that at least 77% of the data lies within
2.085144141 standard deviations of the mean. 

       Since ks = 4,

   2.085144141s = 4 minutes

Divide both sides by 2.085144141

              s =  minutes

              s = 1.918332609 minutes

Round off to however many decimal places your teacher told you,
probably to 1.9 or 1.92 minutes.

Edwin