Find a value of the standard normal random variable z

statistics

Suppose x is a normally distributed random variable with

muμequals=1212

and

sigmaσequals=22.

Find each of the following probabilities.

a.

 P(xgreater than or equals1616)

b.

 P(xless than or equals1010)

c.

 P(13.5213.52less than or equalsxless than or equals17.0417.04)

d.

 P(7.187.18less than or equalsxless than or equals15.5615.56)
 
 
Find a value of the standard normal random variable z, call it
z 0z0,

such that the following probabilities are satisfied.

a.

 P(zless than or equalsz 0z0)equals=0.72277227
b.

 P(minusz 0z0less than or equalszless than or equalsz 0z0)equals=0.80548054
c.

 P(minusz 0z0less than or equalszless than or equals0)equals=0.47864786

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