A Normal Random Variable X Has an Unknown Mean μ

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Examlex · Accepted Answer

The Answer is It is given that x is normally distributed with σ = 2.5 but with unknown mean μ,and
that P (x > 7.5)= 0.8289.In terms of the standard normal random variable z,we can write
P(X > 7.5)= P[Z > (7.5 - μ)/2.5] = 0.8289,Z = -0.95
Since the area to the right of (7.5 - μ)/2.5 is greater than 0.5,then (7.5 - μ)/2.5 must be negative,and that P[(7.5 - μ)/2.5 < z < 0] = 0.3289.Hence,(7.5 - μ)/2.5 = -0.095.This implies μ = 9.875.

A Normal Random Variable X Has an Unknown Mean μ

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