Help!! The summer monsoon rains bring 80% of India's rainfall and are essential for the country's agriculture. Records goingback more than a century show that the amount of monsoon rainfall varies from year to year according to a distributionthat is approximately Normal with mean 852 millimeters (mm) and standard deviation 82 mm. Use the 68- 95- 99.7 ruleto answer the questions.(a) Between what values do the monsoon rains fall in the middle 95% of all years?between 164 and 1540 mmbetween 770 and 934 mmbetween 606 and 1098 mmbetween 688 and 1016 mm (a) Between what values do the monsoon rains fall in the middle 95% of all years?between 164 and 1540 mmO between 770 and 934 mmbetween 606 and 1098 mmbetween 688 and 1016 mm(b) How small are the monsoon rains in the driest 2.5% of all years?less than 21.3 mmless than 688 mmless than 770 mmO less than 606 mm

Name: Help!! The summer monsoon rains bring 80% of India's rainfall and are
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Description: Help!! The summer monsoon rains bring 80% of India's rainfall and are essential for the country's agriculture. Records goingback more than a century show that the amount of monsoon rainfall varies from year to year according to a distributionthat is

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The summer monsoon rains bring 80% of India's rainfall and are essential for the country's agriculture. Records going
back more than a century show that the amount of monsoon rainfall varies from year to year according to a distribution
that is approximately Normal with mean 852 millimeters (mm) and standard deviation 82 mm. Use the 68- 95- 99.7 rule
to answer the questions.
(a) Between what values do the monsoon rains fall in the middle 95% of all years?
between 164 and 1540 mm
between 770 and 934 mm
between 606 and 1098 mm
between 688 and 1016 mm

(a) Between what values do the monsoon rains fall in the middle 95% of all years?
between 164 and 1540 mm
O between 770 and 934 mm
between 606 and 1098 mm
between 688 and 1016 mm
(b) How small are the monsoon rains in the driest 2.5% of all years?
less than 21.3 mm
less than 688 mm
less than 770 mm
O less than 606 mm

Expert Solution

Step 1

The 68-95-99.7 rule states that in a normal distribution 68%, 95% and 99.7% of the values lie within one, two and three

standard deviation around the mean.

The z-scores represent values from the mean in a standard normal distribution.

This transformation is as follows:

z = $\frac{χ - μ}{σ}$

$μ$ is the population mean

$σ$ is the population standard deviation

Because of 68-95-99.7 rule,

we know that approximately 95% of the values for a normal distribution lie between

z = -2 and z = 2,

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