Answer: a) $6,500
Step-by-step explanation:
According to the Chebyshev's Theorem , about
of the values from a data set will wall k standard deviation from mean .
As per given , we have
At least 8/9 of all incomes are in the range of $29,600 to $42,800.
![\mu=\dfrac{\text{Sum of limits}}{2}=\dfrac{29600+42800}{2}=36200](https://tex.z-dn.net/?f=%5Cmu%3D%5Cdfrac%7B%5Ctext%7BSum%20of%20limits%7D%7D%7B2%7D%3D%5Cdfrac%7B29600%2B42800%7D%7B2%7D%3D36200)
i.e.
![k^2=9\\\\ k=\pm 3](https://tex.z-dn.net/?f=k%5E2%3D9%5C%5C%5C%5C%20k%3D%5Cpm%203)
Now in range , lower limit = Mean - k (Standard deviation) = $29,600
⇒ $36,200 - (3)(Standard deviation)= $29,600
⇒ (3)(Standard deviation)= $36,200-$29,600 = $ 6600
⇒ Standard deviation= ( $6600) ÷3 = 2200
Hence, the standard deviation for the auto workers is $6,500.
Thus , the correct answer is a) $6,500 .