Random Variable

Question

A random variable X is distributed normally with E(X) = 8 and σ(X) =3 .

Find P(9≤X<11).

Answer 1

If X~Normal(8,3) then we know that (X-8)/3 ~ Normal(0,1)

 

⇒P(9 < X < 11) = P(9-8 < X-8 < 11-8) = P[(9-8)/3 < (X-8)/3 < (11-8)/3] = P(1/3 < Z < 1)

where Z~Normal(0,1)

 

=P(Z<1) - P(Z<1/3) which can be solved using a Normal table or software

 

Just remember that if you need to find any Normal distribution probabilities, you'll always want to convert it to a Normal(0,1)

 

J.T.