Question

A continuous random variable is normally distributed with a mean of 45 and standard deviation 0f 6. Illustrate the following notations in a normal curve.

P( 30 < X < 50 )

P( 33 ≤ X ≤ 39)

P( X < 57 )

Answer 1

$P(30<X<50)=P(\frac{30-45}{6}<Z<\frac{50-45}{6})=P(-2.5<Z<0.83)=0.7967-0.00621=0.79$

$P(33\le X \le 39)=P(\frac{33-45}{6}<Z<\frac{39-45}{6})=P(-2<Z<-1)=0.158166-0.02275=0.135$

$P(X<57)=P(Z<\frac{57-45}{6})=P(Z<2)=0.9772$