2016 - Demo-Grade 11 Teacher Mass Training

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DENT F CAT ON OF REG ONS

UNDER NORMAL CURVE

JUNE 09, 2016

STAT ST CS AND PROBAB L TY:

NORMAL D STR BUT ON



WHAT WE ARE ABOUT TO LEARN…

Identify e!i"n# $nde t%e n"&'( )$*e)"e#+"ndin! t" diffeent #t'nd'd

n"&'( *'($e#

Find t%e 'e' "f t%e e!i"n ,it%in t%e

n"&'( )$*e-



T%e #%'+e "f t%e n"&'(

di#ti.$ti"n )$*e i# ////////////-

An#,e: Be((0#%'+ed



T%e &e'n1 &edi'n1 'nd &"de 'e

e2$'( 'nd (")'ted 't t%e

///////////-

An#,e: )ente "f t%e

di#ti.$ti"n



T%e )$*e i# #y&&eti)'( '."$t

t%e /////////// 'nd i# ////////////-

An#,e: &e'n3)"ntin$"$#



T%e )$*e ne*e t"$)%e# t%e

///////////-

An#,e: 40'4i#



PROPERTIES OF STANDARD NORMAL DISTRIBUTION

T%e n"&'( di#ti.$ti"n )$*e i#

.e((0#%'+ed-

T%e &e'n1 &edi'n1 'nd &"de 'e e2$'( 'nd

(")'ted 't t%e )ente "f t%e di#ti.$ti"n-

T%e )$*e i# #y&&eti)'( '."$t t%e &e'n-

T%e )$*e i# )"ntin$"$#-

T%e )$*e ne*e t"$)%e# t%e 40'4i#-



Refe t" t%e !'+% .e(",1 identify t%e di#t'n)e "f t%e #%'ded +'t-

Wite t%e 'n#,e "n t%e +'+e !i*en t" y"$-

R'i#e y"$ !"$+# 'n#,e ,it%in 5 #e)#-

67 An#,e: 8





R'i#e y"$ !"$+# 'n#,e ,it%in 5 #e)#-

68 An#,e: 9





R'i#e y"$ !"$+# 'n#,e ,it%in 5 #e)#-

6 An#,e: 7





R'i#e y"$ !"$+# 'n#,e ,it%in 5 #e)#-

6; An#,e: 7-5





R'i#e y"$ !"$+# 'n#,e ,it%in 5 #e)#-

65 An#,e: 7-9



DENS TY CURVE

i# t%e !'+% "f ' )"ntin$"$# +".'.i(ity

'nd &$#t #'ti#fy t%e f"((",in! +"+etie#:

7- T%e t"t'( 'e' $nde t%e )$*e &$#t e2$'( 7-

8- E*ey +"int "n t%e )$*e &$#t %'*e '*eti)'( %ei!%t t%'t i# < " !e'te- =T%'t i#1

t%e )$*e )'nn"t f'(( .e(", t%e 40'4i#->



AREA AND PROBAB L TY

Be)'$#e t%e t"t'( 'e' $nde t%e den#ity )$*e i#

e2$'( t" 71 t%ee i# ' )"e#+"nden)e .et,een 'e'

'nd +".'.i(ity-



THE ?0TABLE



THE ?0TABLE

Y"$ )'n $#e t%e ?0t'.(e t" find ' f$(( #et "f @(e##0t%'n@+".'.i(itie# f" ' ,ide 'n!e "f 0*'($e#- T" $#e t%e ?0

t'.(e t" find +".'.i(itie# f" ' #t'ti#ti)'( #'&+(e ,it%

' #t'nd'd n"&'( =?0> di#ti.$ti"n1 d" t%e f"((",in!:

7- G" t" t%e ", t%'t e+e#ent# t%e "ne# di!it 'nd

t%e fi#t di!it 'fte t%e de)i&'( +"int =t%e tent%#

di!it> "f y"$ 0*'($e-

8- G" t" t%e )"($&n t%'t e+e#ent# t%e #e)"nd di!it

'fte t%e de)i&'( +"int =t%e %$ndedt%# di!it> "fy"$ 0*'($e-

- Inte#e)t t%e ", 'nd )"($&n f"& Ste+# 7 'nd 8-



EAMPLE 6<7

Compute the percent of population between 0 and 0.4

!tart at the row

for 0.4" #ead alon$ until

0.4"

%here i& the 'alue

0.1()6



EAMPLE 6<7 =CONTD…>


1(.)6* of the population arebetween 0 and 0.4 !tandard+e'iation& from the ean.



EAMPLE 6<8

-ercent of -opulation /etween 1 and 2

t the row for 1.0,fir&t column 1.00,there i& the 'alue0.)41)

t the row for 2.0,fir&t column 2.00,there i& the 'alue0.4((2

Note 3rom 1 to 0i& the &ame a& from

0 to 51



EAMPLE 6<8 =CONTD…>


!o 1.* of the population arebetween 1 and 52 !tandard+e'iation& from the ean.

dd the two to $et the total between1 and 2

0.)41) 5 0.4((2 7 0.1



STANDARD NORMAL D STR BUT ON

6* of 'alue& are

within1 &tandard

de'iation of the

mean

9* of 'alue& are

within 2 &tandard

de'iation& of the

mean

99.(* of values are

within ) &tandard

de'iation& of the

mean



PRACT CE 6<7

U#in! t%e +"*ided ?0T'.(e1 find t%e ?0*'($e t%'t)"e#+"nd# t" ;8-88 "f t%e +"+$('ti"n1 '# #%",n-



PRACT CE 6<8

U#in! t%e +"*ided ?0T'.(e1 find t%e ?0*'($e t%'t)"e#+"nd# t" -7 "f t%e +"+$('ti"n1 '# #%",n-



PRACT CE 6<

U#in! t%e +"*ided ?0T'.(e1 find t%e ?0*'($e t%'t)"e#+"nd# t" 78- "f t%e +"+$('ti"n1 '# #%",n-



PRACT CE 6<;

U#in! t%e +"*ided ?0T'.(e1 find t%e *'($e "f t%e#%'ded => t%'t )"e#+"nd# t" ?07-591 '# #%",n-



PRACT CE 6<5

U#in! t%e +"*ided ?0T'.(e1 find t%e *'($e "f t%e#%'ded => t%'t )"e#+"nd# t" ?7-971 '# #%",n-



LETS RECAP…

/////// "f *'($e# 'e ,it%in7 #t'nd'd

de*i'ti"n "f t%e &e'n

/////// "f *'($e# 'e ,it%in 8 #t'nd'd

de*i'ti"n# "f t%e &e'n

/////// "f *'($e# 'e ,it%in #t'nd'd

de*i'ti"n "f t%e &e'n



SOLVE ME

7- Bet,een < 'nd 8-; P=< 8-;>-

8- Bet,een < 'nd J7-K5

P=J7-K5 <>-- T" t%e i!%t "f 7-77 P= 7-77>-

;- T" t%e (eft "f J7- P= J7->-

5- Bet,een 8 'nd 8-;K P=8 8-;K>-

9- Bet,een 7-9 'nd J7-K P=J7-K 7-9>-

K- T" t%e (eft "f 7- P= 7->-

- T" t%e i!%t "f J7-79 P= J7-79>-

U#in! t%e ?0t'.(e +"*ided1 find t%e 'e' $ndet%e #t'nd'd n"&'( )$*e:



ASS GNMENT

E')% &"nt%1 'n A&ei)'n %"$#e%"(d !ene'te# 'n '*e'!e "f

8 +"$nd# "f ne,#+'+e f" !'.'!e " e)y)(in!- A##$&e

t%e #t'nd'd de*i'ti"n i# 8 +"$nd#- A##$&e t%e '&"$nt

!ene'ted i# n"&'((y di#ti.$ted- If ' %"$#e%"(d i# #e(e)ted

't 'nd"&1 find t%e +".'.i(ity "f it# !ene'tin! &"e t%'n

<-8 +"$nd# +e &"nt%-

2016 - Demo-Grade 11 Teacher Mass Training

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