Question

Let X be a continuous random variable distributed by N(7,0.2)N(7,0.2), find:

A) P(X<7.5P(X<7.5 OR X>7.6)=X>7.6)=  Keep your answer in 4 decimal places.

B) P(X≤7.8P(X≤7.8 OR X≥7.8)=X≥7.8)=  Keep your answer in 4 decimal places.

C) P(X≤6.3P(X≤6.3 OR X>6.4)=X>6.4)=  Keep your answer in 4 decimal places.

D) P(X<6.5P(X<6.5 OR X≥7.9)=X≥7.9)=  Keep your answer in 4 decimal places.

Answer 1

a)

P(X<7.5 or X>7.6)

=1-P(7.5<X<7.6)

=1-P((7.5-7)/0.2<Z<(7.6-7)/0.2)
=1-P(2.5<Z<3)
=1-(P(Z<3)-P(Z<2.5))
=1-(0.9987-0.9938)
=1-0.0049=0.9951

b)

P(X≤7.8 OR X≥7.8)=X≥7.8)=1

c)
P(X<=6.3 or X>=6.4)
=1-P(6.3<X<6.4)
=1-P((6.3-7)/0.2<Z<(6.4-7)/0.2)
=1-P(-3.5<Z<-3)
=1-(P(Z<-3)-P(Z<-3.5))
=1-(0.0013-0.0002)=
=1-0.0011 (by using normal table)
=0.9989

d)
P(X<=6.5 or X>=7.9)
=1-P(6.5<X<7.9)
=1-P((6.5-7)/0.2<Z<(7.9-7)/0.2)
=1-P(-2.5<Z<-4.5)
=1-(P(Z<4.5)-P(Z<-2.5))
=1-(1-0.0062)=
=1-9938 (by using normal table)
=0.0062