An airline’s records show that the flights between two cities arrive on average 4.6 minutes late with a standard deviation of 1.4 minutes. At least what percentage of its flights between these two cities arrive anywhere between 1.8 minutes late and 7.4 minutes late?

This problem is solvable with the help of Chebyshev’s theorem. Let’s see how.

Mean = 4.6 Minutes

Standard deviation = 1.4 Minutes

X — Y Range, Where X = 1.8 & Y = 7.4

K = (X – Mean) / SD

Kx = (1.8 – 4.6) / 1.4 = -2

Ky = (7.4 – 4.6) / 1.4 = 2

Probability = 1- 1/(k*k)

= 1 – 1/

1-1/(2*2) = 3/4 = 75%

So Least percentage of flights between two citiies arrive anywhere between 1.8 minutes to 7.4 minutes are

75%

**Chebyshev’s Theorem :** Chebyshev’s Theorem estimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean. This theorem applies to a broad range of probability distributions. Chebyshev’s Theorem is also known as Chebyshev’s Inequality.

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