5.16. The annual rainfall (in inches) in a certain region is normally distributed with u = 40 and o 4. What is the probability that starting withthis year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? What assumptions are you making?

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Asked Nov 21, 2019
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5.16. The annual rainfall (in inches) in a certain region is normally distributed with u = 40 and o 4. What is the probability that starting with
this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? What assumptions are you making?
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5.16. The annual rainfall (in inches) in a certain region is normally distributed with u = 40 and o 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? What assumptions are you making?

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Expert Answer

Step 1

It is given that the annual rainfall in a certain region is normally distributed with mean 40 and standard deviation is 4.

Consider that X is a random variable defined as the annual rainfall.

Thus,

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х - N(и.с) х -N(40,4)

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Step 2

The probability that the rainfall in a year is above 50 inches is:

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X- 50-40 P(x >50) P 4 =P(Z 2.5) 0.0062

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Step 3

The number of years it will take before there is a year occur having over 50 inches rainfall.

Conside...

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Y ~ Geometric (0.0062) P(Y y) 0.0062(1-0.0062) =0.0062x0.9938

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