The annual rainfall (in inches) in a certain region is

snijelihd

snijelihd

Answered question

2021-11-11

The annual rainfall (in inches) in a certain region is normally distributed with μ=40 and σ=4
What is the probability that, starting with this year, it will take over 10 years before a year occurs having a rainfall of over 50 inches? What assumptions are you making?

Answer & Explanation

Michele Tipton

Michele Tipton

Beginner2021-11-12Added 11 answers

μ=40 inches, σ=4 inches. Let X be the normal random variable of the annual rainfall.  
P[X>50]=1P[x50] 
=1P[Xμσ50404] =1P[Z52] =1Φ(52) 
10.9938 =0.0062 
P [non-occurence of rainfall above 50 inches] = 1 - 0.0062 = 0.9938 
P[It will take over 10 years or more before an year with a rainfall above 50 inches]=(0.9938)10

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