Find an approximated probability, Mechanical Engineering

Find an approximated probability:

Sixteen numbers are selected independently and at random from the interval [ 0, 1 ]. Find an approximated probability that the mean of these sixteen, numbers does not exceed 0.6.

Solution:

Let Xi, i = 1, 2, ..., 16 be the selected numbers. Then Xi are i.i.d. each having a uniform distribution on the interval [O, 1 ]. Hence

μ = E (Xi) =1/2 and σ2 = Var Xi =1/12

Hence required probability is

2418_Find an approximated probability.png

=Φ (1.39) = .9177

The utilization of the central limit theorem in approximating a few probability distributions is given in the subsequent section.

Posted Date: 1/31/2013 5:27:38 AM | Location : United States







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