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- FOR A STANDARD NORMAL DISTRIBUTION WE WANT TO FIND C
SUCH THAT THE PROBABILITY OF Z BEING GREATER THAN C = 0.316.
WE'LL FIND THIS Z-SCORE OR THIS VALUE OF C
USING THE TI-84 GRAPHING CALCULATOR.
BUT BEFORE WE DO THIS,
NOTICE HOW WE'RE FINDING A PROBABILITY OF Z
BEING GREATER THAN C AND THEREFORE,
WILL GIVE IT AN AREA TO THE RIGHT OF A Z-SCORE
OF A STANDARD NORMAL DISTRIBUTION,
AND SINCE THE AREA TO THE RIGHT IS LESS THAN 0.5
THE Z-SCORE WILL BE POSITIVE.
SO LET'S SAY THE Z-SCORE
IS MAYBE SOMEWHERE IN HERE WHERE Z = C.
THE PROBABILITY OF Z BEING GREATER THAT C IS = TO 0.316,
WHICH SHOULD BE THE AREA TO THE RIGHT OR THIS AREA HERE.
BUT WHEN USING THE TI-84 GRAPHING CALCULATOR
USING THE INVERSE NORM COMMAND WE MUST ENTER THE PROBABILITY
TO THE LEFT NOT TO THE RIGHT.
SO IF THIS AREA IS 0.316
AND WE KNOW THE AREA UNDER THE STANDARD NORMAL DISTRIBUTION = 1
THEN THE AREA TO THE LEFT, THIS AREA HERE,
WOULD HAVE TO BE 1 - 0.316 OR 1 - THE AREA TO THE RIGHT.
WHICH GIVES US 0.684 FOR THE AREA TO THE LEFT
OR THE PROBABILITY TO THE LEFT OF THIS GIVEN Z-SCORE.
WHEN USING THE INVERSE NORM COMMAND
WE KNOW THE PROBABILITY TO THE LEFT, "COMMA," THE MEAN,
"COMMA," THE CENTER DEVIATION,
BUT IN OUR CASE BECAUSE WE'RE LOOKING FOR A Z-SCORE
WE CAN LEAVE OFF THE MEAN AND STANDARD DEVIATION.
IF WE LEAVE THESE OFF THAN U = 0 AND SIGMA = 1 AND THEREFORE,
IT RETURNS THE Z-SCORE WITH THE GIVEN PROBABILITY.
THE PROBABILITY OF Z BEING LESS THAN C.
SO NOW WE'LL GO TO THE GRAPHING CALCULATOR,
WE'LL PRESS SECOND VARS FOR THE DISTRIBUTION MENU OPTION 3,
AND THEN WE'LL ENTER THE AREA TO THE LEFT
OR THE PROBABILITY TO THE LEFT
WHICH IS 0.684,
CLOSE PARENTHESIS AND ENTER.
THIS IS THE VALUE OF C OR THE Z-SCORE WE'RE LOOKING FOR,
SUCH AS THE PROBABILITY OF Z
BEING GREATER THAN THIS VALUE HERE = TO 0.316.
SO ROUND TO FOUR DECIMAL PLACES. C WOULD BE APPROXIMATELY 0.4789.
SO THE PROBABILITY OF THE GIVEN DATA VALUE
WOULD HAVE A Z-SCORE GREATER THAN 0.4789
IS APPROXIMATELY 0.316 OR 31.6%.
I HOPE YOU FOUND THIS HELPFUL.