- Denote a random variable "X" The annual rainfall (in inches) in a certain region . The random variable follows a normal distribution with parameters mean ( μ ) and standard deviation ( σ ) as follows:

X ~ Norm ( μ , σ^2 )

X ~ Norm ( 40 , 4^2 ).

- The probability that it rains more than 50 inches in that certain region is defined by:

P ( X > 50 )

- We will standardize our test value and compute the Z-score:

P ( Z > ( x - μ ) / σ )

Where, x : The test value

P ( Z > ( 50 - 40 ) / 4 )

P ( Z > 2.5 )

- Then use the Z-standardize tables for the following probability:

P ( Z < 2.5 ) = 0.0062

Therefore, P ( X > 50 ) = 0.0062

- The probability that it rains in a certain region above 50 inches annually. is defined by:

q = 0.0062 ,

- The probability that it rains in a certain region rains below 50 inches annually. is defined by:

1 - q = 0.9938

n = 10 years ..... Sample of n years taken

- The random variable "Y" follows binomial distribution for the number of years t it takes to rain over 50 inches.

Y ~ Bin ( 0.9938 , 0.0062 )

- The probability that it takes t = 10 years for it to rain:

= 10C10* ( 0.9938 )^10 * ( 0.0062 )^0

= ( 0.9938 )^10

= 0.93970

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2 years ago