Monsoons The summer monsoon brings 80% of India’s rainfall and is essential for
ID: 3053003 • Letter: M
Question
Monsoons The summer monsoon brings 80% of India’s rainfall and is essential for the country’s agriculture. Records going back more than a century show that the amount of monsoon rainfall varies from year to according to a distribution that is approximately Normal with mean 852 millimeters (mm) and standard deviation 82mm.
1) In the drought year of 1987, 697 mm of rain fell. In what percent of all years will India have 697 mm or less of monsoon rain?
2) What amount of rainfall represents the 45th percentile of monsoon rains?
3) “Normal” rainfall means within 20% of the long-term average, or between 683mm and 1022mm. In what percent of all years is the rainfall “normal”?
Explanation / Answer
1)
percent of all years will India have 697 mm or less of monsoon rain:
2)
for 45th percentile ; zscore =-0.1257
therefore corresponding value =mean +z*std deviation =852-0.1257*82 =841.70
3)
% of years between 683mm and 1022mm rainfall"
for normal distribution z score =(X-?)/? here mean= ?= 852 std deviation =?= 82.0000