In Manoa Valley on the island of Oahu (Hawaii) the annual rainfall is normally d

Question

In Manoa Valley on the island of Oahu (Hawaii) the annual rainfall is normally distributed with an average of 43.6 inches and standard deviation of 7.5 inches.

a) What is the probability that the annual rainfall for a particular year is more than 56 inches?

b) What is the probability that the annual rainfall for a particular year is less than 32 inches?

c) What is the probability that the annual rainfall for a particular year is between 32 inches and 56 inches?

d) Find the value of rainfall such that 95% of years will have annual rainfall less than this value.

Explanation / Answer

Mean is 43.6 and s is 7.5. z is given as (x-mean)/s

a) P(x>56)= P(z>(56-43.6)/7.5)=P(z>1.65) or 1-P(z<1.65). from normal distribution table we get 1-0.9505=0.0495

b) P(x<32)=P(z<(32-43.6)/7.5)=P(z<-1.55) or 1-P(z<1.55) =1-0.9394=0.0606

c) P(32<x<56)=P(x<56)-P(x<32)=0.9505-0.0606=0.8899

d) for 0.95, the z value is 1.65 from normal table

thus answer is mean+z*s or 43.6+1.65*7.5= 55.975

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