Question

The summer monsoon rains in India follow approximately a Normal distribution with mean 852 millimeters (mm) of rainfall and standard deviation 82 mm.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?A) z = - 1.89B) 97.06%C) 69.7%D) 2.94%

Answer 1

Answer: D) 2.94%

Step-by-step explanation:

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

i.e. $\mu=852$ and $\sigma= 82$

Let x denotes the length of summer monsoon rain.

Then, the probability that India have 697 mm or less of monsoon rain : $P(x\leq697)=P(\dfrac{x-\mu}{\sigma}\leq\dfrac{697-852}{82})\\\\=P(z\leq-1.89)\ \ [\becaiues\ z=\dfrac{x-\mu}{\sigma}]\\\\ = 1-P(z\leq1.89)\ \ [\because\ P(Z<-z)=1-P(Z<z)]\\\\=1-0.9706=0.0294\approx2.94\%$

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

Thus , the correct answer is D) 2.94% .