Question

Suppose x is a normally distributed random variable with

mu μ

equals=3232

and

sigmaσ

equals=99.

Find a value

x 0x0

of the random variable x.

a.

​P(xgreater than or equals≥x 0x0​)equals=.5

b.

​P(xless than<x 0x0​)equals=.025

c.

​P(xgreater than>x 0x0​)equals=.10

d.

​P(xgreater than>x 0x0​)equals=.95

Answer 1

a)

P(X>xo) =0.5

1-P(X<xo)=0.5

P(X<xo)=0.5

for 50th percentile critical value of z=0

therefore corresponding value=mean+z*std deviation=32+0*9 =32

b)

for 2.5th percentile critical value of z=-1.96

therefore corresponding value=mean+z*std deviation=32-1.96*9 =14.36

c )

for 90th percentile critical value of z=1.28

therefore corresponding value=mean+z*std deviation=43.52

d)

for 5th percentile critical value of z=-1.645

therefore corresponding value=mean+z*std deviation=17.20