# Conversions From Lower Tail - HP 10bII+ User Manual

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## Conversions from Lower Tail

The distribution functions on the 10bII+ return values for the lower tail cumulative probability.
The lower tail probability corresponds to the area under the curve to the left of the given value.
Sometimes you will want to work with areas other than the lower tail. It is easy to convert from
lower tail to another area as long as you keep in mind that the total area under the curve is
equal to 1, and the Normal and the Student's T distributions are symmetrical. In other words,
the portion of the curve to the left of zero is a mirror image of the portion of the curve to the
right of zero.
Example 1
The random variable Z is a standard normal random variable. What is the probability that z
is greater than - 1 .7?
The probability that z is greater than - 1 .7 is the area of the curve to the right of - 1 .7. You can
calculate the area to the left of - 1 .7 and subtract it from 1 (total area of the curve).
Table 12-23 Example converting from lower tail
Keys
J7jy]F
y1J4
Figure 17
Display
.044565
.955435
Description
Calculate the lower tail area.
-
Since the area is
1 .7, change
the sign.
Subtracts the lower tail from 1.
Statistical Calculations 133

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