The normal distribution curve shown below is symmetrical abo

The normal distribution curve shown below is symmetrical about the mean and the probability of the shaded portion is given, find the values of a & b.

Solution

assuming WLG tha variance of X is 1 and mean is 0,

then X~N(0,1)

as the distribution is symmetric a and b are mirror of one another, so for any k,

hence, P(-k<x<k)=.7286

that implies k= 1.09984

so b= 1.09984

a= - 1.09984