Answer:
More than 88.889% of the values will fall between 100 and 124 for the data set that has a mean of 112 and a standard deviation of 4.
Step-by-step explanation:
The Chebyshev's theorem states that the probability of any random variable ''X'' assuming a value between a range of ''k times'' the standard deviation is at least
We can write mathematically this as :
P( μ - kσ < X < μ + kσ) (I)
Where μ is the mean and σ is the standard deviation.
In this exercise :
μ = 112
σ = 4
If we replace this values in the equation (I) :
The percent of the values falling between 100 and 124 can be written as :
(II)
This probability must be equal to (III)
Therefore if we work with (II) and (III) ⇒
(II) = (III) ⇒
⇒
⇒ In any of the equations we find that
Finally, we can write that
≅ 88.889%
According to Chebyshev's theorem, more than 88.889% of the values will fall between 100 and 124 for the data set.