Question

Suppose x is a normally distributed random variable with muequals12 and sigmaequals2. Find each of the following probabilities. a.​ P(xgreater than or equals15​)   b.​ P(xless than or equals8​)   c.​ P(12.52less than or equalsxless than or equals16.74​)   d.​ P(7.6less than or equalsxless than or equals15.1​)

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	12
std deviation   =σ=	2.0000

P(xgreater than or equals15​) :

probability =

P(X>15)

=

P(Z>1.5)=

1-P(Z<1.5)=

1-0.9332=

0.0668

b)

P(xless than or equals8​) :

probability =

P(X<8)

=

P(Z<-2)=

0.0228

c)

P(12.52less than or equalsxless than or equals16.74​) :

probability =

P(12.52<X<16.74)

=

P(0.26<Z<2.37)=

0.9911-0.6026=

0.3885

d)

probability =

P(7.6<X<15.1)

=

P(-2.2<Z<1.55)=

0.9394-0.0139=

0.9255