Question

Consider a sample with a mean of 30 and a standard deviation of 5. Use chebyshev's theorem to determine the percentage of data within 15 to 45.

Answer 1

With the help of Chebyshev's theorem, the percentage of data between 5 to 45 is 89%.

What is Chebyshev's theorem?

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem.

Numerous other probability distributions can be applied to this theorem.

Chebyshev's Inequality is another name for Chebyshev's Theorem.

One of many theorems established by Russian mathematician Pafnuty Chebyshev is known as Chebyshev's theorem.

According to Bertrand's postulate, there is a prime between n and 2n for every n.

So, the percentage of data within 15 to 45 is:

In this instance, we're looking for numbers between 15 and 45.

Since 30 -3*5 = 20 and 30 + 3*5 = 45, we are therefore within 3 deviations of the mean. So, since k = 3, we can find the percent as follows:

% = (1 - 1/3²) × 100 = 88.88% = 89%

Therefore, with the help of Chebyshev's theorem, the percentage of data between 5 to 45 is 89%.

Know more about Chebyshev's theorem here:

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