SOLUTION: X is a normally distributed random variable with a mean of 5.0. Find the standard deviation of the distribution if 59.10% of the data lies to the right of 4.54.

Question 1085351: X is a normally distributed random variable with a mean of 5.0. Find the standard deviation of the distribution if 59.10% of the data lies to the right of 4.54.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We are given
:
Probability(P) ( X > 4.54 ) = 1 - P ( X < 4.54) = 0.591
:
P ( X < 4.54 ) = 1 - 0.591 = 0.409
:
we check z-tables for the z-score associated with 0.409
:
z-score is -0.23
:
we know
:
(4.54 - 5) / standard deviation = -0.23
:
*******************************************
standard deviation = (4.54 - 5) / -0.23 = 2
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:

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