There is a 88.4% chance that my value of x is 30 or greater. If I assume my data is normally distributed..

Question

There is a 88.4% chance that my value of x is 30 or greater. If I assume my data is normally distributed, can I determine the likelihood that my value of x is 26, 27, 28, 29, 31, 32, 33, 34 etc?

 

If so, how?

Answer 1

given:  Prob ( X >=30) = 0.884

 

You want the probability that X is NOT 30

 

Prob(X>=30) = 0.884 is given

 

-Prob (X>=30) = -0.884   <--- multiplies both sides by -1

 

1-prob(x>=30) = 1-0.884 = 0.116 <--- adds 1 to both sides

 

Prob (X <30) = 0.116 <--- property of normal bell curve

 

Using this same probability, doing a REVERSE lookup 

On the normal distribution table, P(z< K) = 0.116 corresponds to Z=-1.221

which is the same as X=30. That is,  z=-1.221 is the corresponding z-score for X=30.

 

The probability that X=30 exactly can be approximated with the

continuity correction Prob ( 29.5 < X < 30.5) =

                               Prob (     -1.23    < z < -1.20) <---  *** Be careful here!!!

                               = Prob ( z < -1.20) - Prob ( z < -1.23)

                                = 0.1151 - 0.1112

                                = 0.0039

 

which is the smallest continuity correction offered by the normal distribution table

that is available.

 

Therefore,

 Prob ( X is not 30) =

Prob ( X < 30) + Prob(x>=30) - Prob(X=30)

= 0.1116 + .884 - 0.0039

= 0.9917

= 99.17%