Answer: a) $6,500
Step-by-step explanation:
According to the Chebyshev's Theorem , about [tex](1-\dfrac{1}{k^2})[/tex] 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.
[tex]\mu=\dfrac{\text{Sum of limits}}{2}=\dfrac{29600+42800}{2}=36200[/tex]
i.e. [tex](1-\dfrac{1}{k^2})=\dfrac{8}{9}[/tex]
[tex]\dfrac{1}{k^2}=1-\dfrac{8}{9}=\dfrac{1}{9}[/tex]
[tex]k^2=9\\\\ k=\pm 3[/tex]
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 .
It can be deduced that the standard deviation for the auto workers is $2200.
From the information given, it can be noted that:
P (29600 < x < 42800) > 8/9
where, x = random variable
By Chebyshev's Theorem, we will have:
k = 3
Mean = 29600
(u + 3sd) - (u - 3sd) = 42800 - 29600
6sd = 13200
SD = 13200/6
SD = $2200
In conclusion, the standard deviation is $2200.
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