For a standard normal distribution, find p(z>c)=0.6289 find c

Question

Use the z table

Answer 1

p(Z>c)=1-p(Z<c).

The tables give values for Z<c, and for p=0.6289, c=0.3289 approx.

Graphically the p value is the area under the normal distribution curve to the left of the Z value. We want the area to the right, which is about 63% of the results, so since the total area (probability) is 1 and the curve is symmetrical, we need the value of Z for p=1-0.6289=0.3711. This is less than 0.5 (50%), the central point (maximum, median, mean, or highest point) being Z=0. Therefore Z is negative and c=-0.3289.