Page 61 - Math SL HB Sem 3

Finding'a',' p' or.o, (lnverse normal distribution):
lL ('

lf we are given the probabilities and any two of the 'a, or,p' or,o,,
we can figure oul the remaining one using the inverse normal distribution E
il

P a

) Finding a (GDC optional) - problem solving flow chart:

p(X p(X
Translate the given informalion into X-N (p,o2) and < a) or > a)

Sketch the curve, mark where.a'should be and shade the relevant region.

For P(X < a) > 0.5
For P(X > a) > 0.5

X x
I
a

or P(X > a) < 0.5
or P(X < a) < 0.5

< 0.5 < 0.5

X X
a
Q

'a' lies to the right of lhe mean
'a' lies to the left of the mean

a>