282
UTPN(mean,variance,value)
This function, the ‘Upper-Tail Probability
(Normal)’, gives the probability that a
normal random variable is greater than or equal to the value supplied. Note
that the variance must be supplied, NOT the
standard deviation.
Eg. 1. Find the probability that a randomly
chosen individual is more than 2 meters
tall if the population has a mean height
of 1.87m and a standard deviation of
10.4cm
2
1.87 , 0.104
0.010816
mm
σ
σ
==
⇒=
Ans: P(height>2m) = 0.1056
Eg. 2. The population of Year 12 Applicable Mathematics students had a
mean exam score of 65% and a standard deviation of 14%.
What two scores will cut off the top and bottom 10% of students?
i.e. Find
0
such that
0
()01Px x>=⋅
Using the Solve aplet (right) we can reverse
the normal direction of the UTPN function.
Enter the expression to be solved for into the
SYMB view as shown above, then switch to the
numeric view. Enter a guess of 0.8 (80%) and
then press .
The second value can be found by using the
symmetry properties of the Normal
Distribution, but it is probably just as fast to go
back to the SYMB view, change the 0.1 to 0.9
and then re-Solve. Remember that an
key is provided in the SYMB view to allow you
to change the expression without having to retype it.
Final answer… 47.06% and 82.94% are the cut-offs.
2m
0·1
65%
0·1
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