Respuesta :
The Probability P [tex](20\leq x\leq 36)[/tex] = 0.7500
What is probability ?
The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence may be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
Given : the mean μ = 28
standard deviation σ = 4
small value = 20 and big value = 36
by chebychev's inequality,
μ - kσ = small value
28-k(4) = 20
k = 2
also,
μ + kσ = big value
28 + k(4) = 36
k = 2
The Probability P [tex](20\leq x\leq 36)[/tex] = [tex]1-1/k^{2}[/tex]
[tex]= 1-1/2^{2} \\=3/4\\=0.7500[/tex]
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