Page 58 - Math SL HB Sem 3

Finding the cumulative probabilities, p :

Given the mean, standard deviation, and the upper or lower limit (denoted as'a') of a random variable,
we can find the conesponding cumulative probabilities.

)Problem solving flow chart:
^& Extract p and d from the question and write down X -N (p oz).
,
ln Paperl:

-b* Transform X to Z by lhe standardising relation: 2 =!-!.

Sketch the curve and shade the region for the unknown cumulative probability

,,_ Identify how the unknown cumulative probability is related to the case where
- +r+ ti.
1
), P (Z < a)tor a is a positive value using the symmelrical properties of the curve.
-!i+- Use lhe table in lhe formula booklel to read off the value oi p(Z S a), where a
'I
is positive.
E.g. Reading ott P(z < 0.18) from the tabte:

p=P(Z<z) P

Z
a
z 0 0.01 0.02 0.03 0.04 0.05 0.06 o.o7 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5150 0.s199 0.s239 0.5319 0.5359
0.1 0.s389 0.5438 o.s47a o.5517 0.55s7 0.s96 0.5636 J05279 0.5714 0.5753
0.5675

'i:.;j*' Work out the unknown cumulative probability.

ln Paper 2

Calculator-T ' DIST, - ,normalcdf
(lower limit, upper limit, mean, standard deviation), ;
.normal
Calculator€: go to c,d.' ;
No need to transfom X lo Zl
P(X 3 a)) set the lower limit as -1e^99 and enter the upper limit, a, the mean and
standard deviation accordingly.

P(x > a) ) set the upper rimit as r.e^99, enter the rower rimit, a, the mean and standard
deviation accordingly.
1

{, Note:

For examinatlons in 2014 and thereafler, probabilities and values ofthe variable must be found using
technology

,?