According to chebyshev's theorem, what percent of the values will fall between 100 and 124 for a data set that has a mean of 112 and a standard deviation of 4?

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.

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