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Z table

Information   Inverse Z table   example

p(X ≤ x) = ?
Z00.010.020.030.040.050.060.070.080.09
00.50.50398935630.50797831370.51196647340.51595343690.51993880580.52392218270.52790317020.5318813720.5358563926
0.10.53982783730.54379531250.5477584260.55171678670.55567000480.55961769240.56355946290.56749493170.57142371590.5753454347
0.20.57925970940.58316616350.58706442260.59095411510.59483487170.59870632570.60256811320.60641987320.61026124760.6140918812
0.30.61791142220.62171952180.62551583470.62930001890.6330717360.63683065120.64057643320.64430875480.64802729240.6517317265
0.40.65542174160.65909702620.66275727320.66640217940.67003144630.67364477970.67724188970.68082249120.68438630350.6879330506
0.50.69146246130.69497426910.69846821250.70194403460.70540148380.70884031320.71226028120.7156611510.71904269110.7224046752
0.60.72574688220.72906909620.73237110650.73565270790.73891370030.74215388920.74537308530.74857110490.75174776950.7549029063
0.70.75803634780.76114793190.76423750220.76730490770.77035000280.77337264760.77637270760.77935005370.78230456240.7852361158
0.80.78814460140.79102991210.79389194640.79673060820.79954580670.80233745690.80510547870.80784979790.81057034520.813267057
0.90.81593987470.81858874510.82121362040.82381445780.82639121970.82894387370.83147239250.83397675390.83645694070.8389129405
10.84134474610.8437523550.84613576960.84849499720.85083004970.85314094360.85542770030.85769034560.85992890990.862143428
1.10.86433393910.86650048680.8686431190.87076188780.87285684940.87492806440.87697559690.87899951560.88099989250.882976804
1.20.88493032980.88686055360.88876756260.89065144760.89251230290.89435022630.89616531890.89795768490.8997274320.901474671
1.30.90319951540.90490208220.9065824910.90824086430.90987732750.91149200860.91308503810.91465654920.91620667760.9177355613
1.40.91924334080.92073015850.92219615950.92364149050.92506630050.92647074040.9278549630.9292191230.93056337670.931887882
1.50.93319279870.93447828790.93574451220.93699163550.93821982330.9394292420.94062005940.94179244440.94294656680.9440825975
1.60.94520070830.94630107190.94738386150.94844925150.94949741650.9505285320.95154277370.95254031820.95352134210.9544860227
1.70.95543453720.95636706350.95728377920.95818486240.9590704910.95994084310.96079609670.96163642960.96246201970.9632730443
1.80.96406968090.96485210640.96562049760.96637503060.96711588130.96784322520.9685572370.96925809110.9699459610.97062102
1.90.97128344020.97193339330.97257105030.97319658110.97381015510.97441194050.97500210490.97558081470.97614823570.9767045322
20.97724986810.97778440560.97830830620.97882173040.97932483710.97981778460.98030072960.98077382780.98123723360.9816911001
2.10.98213557940.98257082210.98299697740.98341419330.98382261660.98422239260.98461366520.9849965770.98537126920.9857378816
2.20.98609655250.98644741890.98679061620.98712627860.98745453860.98777552730.98808937460.98839620850.98869615580.9889893417
2.30.989275890.98955592290.98982956130.99009692440.99035813010.99061329450.99086253250.99110595740.9913436810.9915758136
2.40.99180246410.99202373970.99223974640.99245058860.9926563690.99285718930.99305314920.99324434740.99343088090.9936128452
2.50.99379033470.99396344190.99413225830.99429687370.99445737660.9946138540.99476639180.99491507430.99505998420.9952012034
2.60.9953388120.99547288890.99560351170.99573075660.99585469860.99597541150.99609296740.99620743770.9963188920.996427399
2.70.99653302620.99663583960.99673590420.99683328370.99692804080.99702023680.99710993190.99719718540.99728205510.9973645979
2.80.99744486970.9975229250.99759881750.99767259980.99774432330.99781403850.9978817950.9979476410.99801162410.9980737909
2.90.99813418670.99819285620.99824984310.998305190.99835893880.99841113040.99846180480.99851100130.99855875810.9986051128
30.9986501020.99869376160.99873612660.99877723130.99881710930.99885579320.9988933150.99892970610.9989649970.9989992175
3.10.99903239680.99906456330.99909574480.99912596850.99915526080.99918364770.99921115430.99923780530.99926362470.999288636
3.20.99931286210.99933632510.9993590470.99938104890.99940235150.9994229750.99944293890.99946226260.99948096460.9994990631
3.30.99951657590.99953352010.99954991280.99956577010.99958110810.99959594220.99961028760.99962415910.99963757090.9996505369
3.40.99966307070.99967518560.99968689430.99969820940.99970914290.99971970670.99972991230.99973977080.99974929310.9997584897
3.50.99976737090.99977594670.99978422660.99979222020.99979993650.99980738440.99981457260.99982150940.99982820290.999834661
3.60.99984089140.99984690150.99985269850.99985828940.9998636810.99986887980.99987389240.99987872480.9998833830.999887873
3.70.99989220030.99989637040.99990038860.99990426010.99990798990.99991158270.99991504330.99991837620.99992158580.9999246764
3.80.9999276520.99993051660.99993327420.99993592840.99993848280.99994094110.99994330650.99994558230.99994777180.9999498779
3.90.99995190370.99995385190.99995572550.99995752710.99995925920.99996092440.99996252510.99996406370.99996554240.9999669634
40.99996832880.99996964060.99997090090.99997211160.99997327440.99997439120.99997546360.99997649340.99997748210.9999784313
4.10.99997934250.9999802170.99998105640.99998186180.99998263470.99998337620.99998408760.999984770.99998542450.9999860523
4.20.99998665430.99998723150.99998778490.99998831540.9999888240.99998931150.99998977870.99999022640.99999065530.9999910663

Inverse Z table

Calculates the inverse cumulative distribution.

Z1-α=-Zα

> example
αZαZ1-αZα/2Z1-α/2
0.001-3.0902323.090232-3.2905273.290527
0.0025-2.8070342.807034-3.0233413.023341
0.005-2.5758292.575829-2.8070342.807034
0.01-2.3263482.326348-2.5758292.575829
0.025-1.9599641.959964-2.2414032.241403
0.05-1.6448541.644854-1.9599641.959964
0.1-1.2815521.281552-1.6448541.644854
0.15-1.0364331.036433-1.4395311.439531
0.2-0.8416210.841621-1.2815521.281552
0.25-0.674490.67449-1.1503491.150349
0.3-0.5244010.524401-1.0364331.036433
0.35-0.385320.38532-0.9345890.934589
0.4-0.2533470.253347-0.8416210.841621

Information

This is the 21st century, for any practical use you can use the normal distribution calculator instead of the tables. Just choose x: for the Z-table or P(X≤x) for the inverse z-table.

Z table
The Z-table contains the probabilities that the random value will be less than the Z score, assuming standardnormal distribution.
The Z score is the addition of the lett column and the upper row.

Example:
Z score equals 0.32
Row 4 (0.3) and column 3 (0.02). 0.32 = 0.30 + 0.02
P(X ≤ 0.32) = 0.6255158347
P(X ≤ -0.32) = 1- P(X ≤ 0.32) = 0.3744841653

Inverse Z table:
Calculates the Z score based on the less than or greater than probabilities
α - contains the probability.
Zα - the Z-value where p(X≤Zα) = α, critical value of the left-tailed test.
Z1-α - the Z-value where p(X≥Z1-α) = α, critical value of the right-tailed test.
Zα/2 - the Z-value where p(X≤Zα/2) = α/2, left critical value of the two-tailed test.
Z1-α/2 - the Z-value where p(X≥Z1-α/2= α/2, right critical value of the two-tailed test.

Example:
Row number 6
P( X ≤ -1.644854 ) = 0.05,  P( X ≥ 1.644854 ) = 0.05,  P( X ≤ -1.959964 ) = 0.025,  P( X ≥ 1.959964 ) = 0.025