Question

3. Monsoon Rains in Indonesia is normally distributed over the years.:

Normal amount of rainfall with a mean 800 millimeters (mm) and standard deviation 80 mm.

Compute the Probability of the rainfall exceeding 720 mm?

How small are the Monsoons rains in the driest 2.5 % of all years: ________________

Determine the Median amount of rainfall over the years.

Answer 1

Part a)

X ~ N ( µ = 800 , σ = 80 )
P ( X > 720 ) = 1 - P ( X < 720 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 720 - 800 ) / 80
Z = -1
P ( ( X - µ ) / σ ) > ( 720 - 800 ) / 80 )
P ( Z > -1 )
P ( X > 720 ) = 1 - P ( Z < -1 )
P ( X > 720 ) = 1 - 0.1587
P ( X > 720 ) = 0.8413

Part b)

X ~ N ( µ = 800 , σ = 80 )
P ( X < x ) = 2.5% = 0.025
To find the value of x
Looking for the probability 0.025 in standard normal table to calculate Z score = -1.96
Z = ( X - µ ) / σ
-1.96 = ( X - 800 ) / 80
X = 643.2 mm
P ( X < 643.2 ) = 0.025

Part c)

X ~ N ( µ = 800 , σ = 80 )
P ( X < x ) = 50% = 0.5
To find the value of x
Looking for the probability 0.5 in standard normal table to calculate Z score = 0
Z = ( X - µ ) / σ
0 = ( X - 800 ) / 80
X = 800
P ( X < 800 ) = 0.5

Median = 800 mm