Given that X inormally distributed with a mean of 0545 and a

Given that X inormally distributed with a mean of 0.545 and a standard deviation of 0.155, calculate the probability that X exceeds 0.5

Solution

using the formula of standardized variable Z

that is Z = ( xbar - miu ) / sigma

we will find the probability in the tables of Z distribution

P( x > 0.5)

P( z > (0.5-0.545) / 0.155)

P( z >-0.29 ) = 1 - P( z < -0.29) = 1 -0.3859 =0.6141