1. The summer monsoon rains in India follow approximately a Normal distribution

Question

1. The summer monsoon rains in India follow approximately a Normal distribution with mean 852 millimeters (mm) of rainfall and standard deviation 82 mm Note: You are working with a continuous random variable. 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? b. "Normal rainfall" means within 20% of the long-term average, or between 683 mm and 1022 mm. In what percent of all years is the rainfall normal? c. Less than how much rain falls in the driest 8% of all year?

Explanation / Answer

Here mean =852 and sd=82

a. P(x<=697)=P(z<697-852/82)=P(z<=-1.89)=0.0294

b. P(683<x<1022)=P(-2.06<z<2.07)=0.9611

c. P(X<x)=0.08

Using z table we get z=-1.405

As we know z=x-mu/sd=-1.405

X=736.79

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