Question

3.11 Monsoon Rains. The summer monsoon rains in India follow approximately a Normal distribution with mean 852 millimeters (mm) of rainfall and standard deviation 82 mm.

(a) In the drought year 1987, 697 mm of rain fell. In what percent of all years will India have 697 mm or less of monsoon rain? PLEASE THOROUGHLY EXPLAIN STEP BY STEP SOLUTION.

(b) “Normal rainfall” means within 20% of the long-term average, or between 682 mm and 1022 mm. In what percent of all years is the rainfall normal? PLEASE THOROUGHLY EXPLAIN STEP BY STEP SOLUTION.

Answer 1

Mean = = 852

Standard deviation = = 82

a)

We have to find the percent of all years will India have 697 mm or less of monsoon rain.

That is we have to find P(X 697)

For finding this probability we have to find z score.

That is we have to find P(Z - 1.89)

P(Z - 1.89) = 0.0294

( From z table)

2.94% of all years will India have 697 mm or less of monsoon rain.

b)

We have to find the percent of all years is the rainfall normal.

The "Normal rainfall" is between 682 mm and 1022 mm.

First we have to find P( 682 < X < 1022)

For finding this probability we have to find z score.

That is we have to find P( - 2.07 < Z < 2.07)

P( - 2.07 < Z < 2.07) = P(Z < 2.07) - P(Z < - 2.07) = 0.9809 - 0.0191 = 0.9618

( From z table)

96.18% of all years is the rainfall normal.