Question

from a sample with n equal 36 the mean duration of a geyser eruptions is 3.69 minutes and the standard deviation is .61 using chebchev theorem determine at least how many of the eruptions lasted between 1.86 and 5.53 minutes

Answer 1

Mean, = 3.69

Standard deviation, = 0.61

Now, 1.86 = 3.69 - 1.83 =

5.53 = 3.69 + 1.84 =

From Chebyshev's theorem, the proportion of values that fill within k standard deviations of the mean will be at least

Thus, the proportion of eruptions which will last between 1.86 and 5.53 minutes ≥ = 8/9 ≈ 88.9%

Now, 36*8/9 = 32

Thus, atleast 32 out of 36 eruptions lasted between 1.86 and 5.53 minutes