The summer monsoon rains in a country follow approximately a Normal distribution with mean 857 millimeters (mm) of rainfall and standard deviation 85 mm. (Round your answers to two decimal places.)
(a) In a drought year, 699 mm of rain fell. In what percent of all years will this country have 699 mm or less of monsoon rain?

And we can find this probability using Excel or the normal standard table:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the summer monsoon rains of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using Excel or the normal standard table:

2

step-by-step explanation: