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- FOR A STANDARD NORMAL DISTRIBUTION,
WE WANT TO FIND C SUCH THAT THE PROBABILITY OF Z
BEING LESS THAN C IS EQUAL TO 0.614,
WHICH MEANS IF WE SELECTED A RANDOM DATA VALUE,
THE PROBABILITY THAT THE Z-SCORE BE LESS THAN C
WOULD BE 0.614 OR 61.4%.
WE'LL FIND C BY USING THE CUMULATIVE Z-SCORE TABLE
PROVIDED HERE BELOW.
BUT BEFORE WE DO THIS,
NOTICE HOW THIS PROBABILITY IS GREATER THAN 50%,
SO WE SHOULD NOTICE THAT THE Z-SCORE WOULD BE POSITIVE
BECAUSE WHEN Z IS ZERO, DATA VALUE WOULD BE THE MEAN
AND THEREFORE, 50% OF THE DATA WOULD BE LESS THAN Z = 0
AND 50% WOULD BE GREATER THAN Z = 0.
SO NOW LOOKING AT OUR TABLE BELOW,
WE'RE LOOKING FOR OUR PROBABILITY
OR AN AREA UNDER THE STANDARD NORMAL DISTRIBUTION OF 0.614.
THE CLOSEST VALUE IS HERE AT 0.6141.
NOTICE HOW THE Z-SCORE FOR THIS PROBABILITY
FOR THIS AREA WOULD BE 0.29.
SO WE'LL SAY C IS APPROXIMATELY 0.29.
SO IF WE GO BACK OVER TO THE STANDARD NORMAL DISTRIBUTION
HERE ON THE RIGHT,
IF WE FIND Z = 0.29,
LET'S SAY IT'S APPROXIMATELY HERE.
THEN THE AREA TO THE LEFT UNDER OUR CURVE
WOULD BE APPROXIMATELY 0.614,
WHICH WOULD ALSO BE THE PROBABILITY
THAT A RANDOMLY SELECTED DATA VALUE WOULD HAVE A Z-SCORE
LESS THAN 0.29.
I HOPE YOU FOUND THIS HELPFUL.