A probability distribution has a mean of 27 and a standard deviation of 2. Use Chebychev's inequality to estimate the probability that an outcome of the experiment lies between 20 and 34. a) 0.2857 b) 0.9945 c) 0.0816 d) 0.0055 e) 0.9184 f) None
z-score = (X - mean ) / SD
For X = 20 ,
Z = (20 - 27) / 2
= -3.5
For X = 34
Z = ( 34 - 27) / 2
= 3.5
That is 20 and 34 are 3.5 standard deviation of the mean.
z = k = 3.5
Using chebyshev inequality
P( | X -
| >= k
) <= 1 - 1/k2
So,
P(20 < X < 34) = 1 - 1/3.52
= 0.9184
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Assume that x has a...