Hi

can I have this checked please - say if n = 4
mean = 16.2 and SD = 0.12 / 2 = 0.06
P = (M<16)
= P (   (M-16.2) / 0.06 < (16 - 16.2) / 0.06)
= P (         Z         < (16-16.2)/ 0.06)
= -0.20 / 0.06 = -3.33
= .4996

I would really appreciate if someone can confirm if I have used the
right methodology
Elshana

Hi elshana!!

You have the following data:
n = 4; (this info is useless to this problem).
mean = 16.2;
SD = 0.06
Normal Distribution.
And you want to know the probability of the event (M < 16).

In this kind of problems you must start with the transformation of the
normal random variable M into the standard normal variable Z:

Z = (M - mean)/ SD = (16 - 16.2)/0.06 = -0.2 / 0.06 = -3.33

Now using the Normal distribution tables you can calculate what you
want:

P(M < 16) = P(Z < -3.33)

This is the area under the area under the standard normal curve from
-3.33 to -oo, by the simmetry if the normal distribution we have that
this is the same area under the standard normal curve from 3.33 to
+oo, then, after consulting the normal distribution table, we have:

P(M < 16) = P(Z < -3.33) = P(Z > 3.33) =

P(Z > 3.33) = P(0 < Z) - P(0 < Z < 3.33) = 0.5 - 0.4996 = 0.0004

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

"The Standard Normal Distribution":
http://www.oswego.edu/~srp/stats/z.htm

"Normal Distribution":
http://www.stat.wmich.edu/s216/normal/normal.html

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


I hope this helps you. If you need a clarification, please ask for it
before rate this answer.

Best regards.
livioflores-ga

thank you for your clarification
elshana