Page 59 - Math SL HB Sem 3

Detailed exploration of cases 1-4 :
)When a is positive:

case lt P(Z < a)
There is no difference
betweenP(Z 3 a) or
P(Z < o)
i.e. 'o' lies to the right ofthe
mean
z
Case2: P(Z 2 a\ ct

P(Z>a)=L- P(Z<a)
To flip the inequality sign from 2 to S, subtract from 1.

P(Z > a) Area under
curve
g
-l
Z z Z
{l d
)When a is negative:

i.e. d' lies to the left of the
mear
case 3: P(Z < @)
Area under curve is
the same by
symmetry
P(Z < a)
Z Z
a -a
P(z<a)=P(Z>-a)
=r- P(z=-o-) --.. (-o) is positive.
case 4t P(Z > a) )same as case 2

Area under curve i5
the same by
symmetry
,Z
z
-a
CL
P(Z > a): P(Z < q)

To change 'a'from negative to positive, flip the inequality sign!

C}
&' Note:

You should be able to figure out cases 5-7 with the knowledge above'

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