Question:
p(z>c)=.2546
Solution:
Z is a standard normal variable usually available on calculators or standard tables. The function has a domain of (-∞,+∞), and it looks like the following:
The value of c can be read as 0.6601.
In the case of a table, which are normally given to the left tail, as shown:
http://isites.harvard.edu/fs/docs/icb.topic1499785.files/Public%20Domain%20Normal%20Distribution%20Table.pdf
Since we need the right tail (Z>c), we subtract the value 0.2546 from one to get 0.7454, and look up the value from the table, which corresponds to the value 0.66, as shown in red.
It is possible to calculate the value to a higher precision using statistical software such as R. The commands to use could be:
qnorm(0.2546,lower.tail=FALSE);
or
qnorm(1-0.2546)
for the same reasons as explained using the table.
The latter statement makes use of the fact that the upper tail is the complement of the lower, hence subtract from one.
The result R gives is 0.6600839, as follows:
> qnorm(0.2546,lower.tail=FALSE)
[1] 0.6600839
> qnorm(1-0.2546)
[1] 0.6600839
>