Gaussian distribution A Gaussian random variable X has param

Gaussian distribution] A Gaussian random variable X has parameters mu x = 4 and sigma X = 2. Find P(|X| > 2). Also find P(|X|ge 2).

Solution

A random variable X has Gaussian distribution with parameter µ_x = 4 and _x = 2.

A Gaussian distribution is nothing but the normal distribution.

We have to calculate P( IXI > 2 ) and P ( IXI 2 ).

P( IXI > 2 ) = P( -2 < X < 2)

= P( (-2 - µ) / < (X- µ ) / < (2 - µ ) / )

= P ( (-2 - 4) / 2 < Z < (2 - 4) / 2 )

= P ( -3 < Z <-1 )

= P ( Z < -1) - P ( Z < -3)

This probability we can calculate using EXCEL.

Command : =NORMDIST(z)

= 0.158655 - 0.00135

= 0.157305

P( IXI 2) = P ( -2 X 2 )

= P ( X 2 ) - P ( X -2)

= P ( X -1 ) - P ( X -3)

= 0.157305