X is normal random variable
mean = 20
STD dev. = 4
find Prob.
P(X<29)
P(X=40)
P(14<X<=29)

REGARDS
JABEDA

Hi jabeda!! 

We must start with the transformation of the
normal random variable M into the standard normal variable Z:
 
Za = (a - mean)/ SD ;

After that using the Normal distribution tables you can calculate what
you
want:
P(X < a) = P(Z < Za).

For a table see:
"Normal Distribution Table": 
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/normaltable.html


For reference see the following page: 
"USING THE STANDARDIZED NORMAL DISTRIBUTION TABLE": 
http://myphliputil.pearsoncmg.com/student/bp_berenson_bbs_9/section6_1.pdf


--------------------------------------------------

P(X<29):

Z = (29 - 20) / 4 = 9/4 = 2.25

P(X < 29) = P(Z < 2.25) = P(Z < 0) + P(0 =< Z < 2.25) = 
          = 0.5 + 0.4878 = (see the table)
          = 0.9878

----------------------------------------------------

P(14<X<=29):

Z1 = (14 - 20) / 4 = -7/4 = -1.75
Z2 = (29 - 20) / 4 = 9/4 = 2.25

P(14 < X <= 29) = P(-1.75 < Z =< 2.25) =
                = P(-1.75 < Z < 0) + P(0 < Z < 2.25) =
                = P(0 < Z < 1.75) + 0.4878 =
                = 0.4599 + 0.4878 = (see the table)
                = 0.9477

------------------------------------------------------

P(X = 40) = 0

This is because for a continuous random variable the probability for
assuming any specific value is zero.
P(X = x) = 0 for all x, that means the probability distribution of a
continuous random variable cannot be represented by its point
probabilities (as in the discrete case).
"...Is it true that P(X = a) is zero for every number a in the
interval associated with X?
Answer: 
As a general rule, yes. If X is a continuous random variable, then X
can assume infinitely many values, and so it is reasonable that the
probability of its assuming any specific value we choose beforehand is
zero."
From "Calculus Applied to Probability and Statistics" by Stefan Waner
and Steven R. Costenoble:
http://people.hofstra.edu/faculty/Stefan_Waner/cprob/cprob1.html

----------------------------------------------------------

I hope this helps you. Feel free for ask for request for an answer
clarification if it is needed.

Best regards.
livioflores-ga

thank you very much for your quick response and clarification
regards
jabeda