Let X be the amount of rainfall in mm
It is given that X follows a normal distribution. What is not known is the mean and the standard deviation of rainfall.
You're given
= 0.877.
1. Draw a bell-shaped curve and illustrate that.
2. Then look up in a standard normal table and find the z value that corresponds to a p value of 0.877.
3. Is it a positive z or a negative value? You'll know when you look at your drawing. In fact, it is strongly advised to draw a picture.
4. So then you use the formula
to obtain a first equation involving
and
.
Repeat as from step 1. for the other piece of information
= 0.409.
Draw a picture for that too. Look up the z value corresponding to a p value of 0.409 in normal tables or use Excel Norminv function.
You should get two simultaneous equations with
and
as two unknowns and solve to get them.
Then armed with these values, you can calculate
.