Question

if The number of days with precipitation amounts to 0.01 inches what is the probability of having exactly 10 days of precipitation in the month of April? What is the probability of having less than three days of precipitation in the month of April? What is the probability of having more than 15 days of precipitation in the month of April?

Answer 1

Here mean number of days with precipitation amounts to 0.01 inch is not given.

Let's assume that mean number of days with precipitation amounts to 0.01 inch in the month of April = = 9.5 days.

a) what is the probability of having exactly 10 days of precipitation in the month of April?

Let X = number of days of precipitation in the month of April

So X follows Poisson distribution with parameter = 9.5

(Note that : You can use given value of mean in the original example instead of = 9.5 )

The probability of having exactly 10 days of precipitation in the month of April = P( X = 10 )

Let's use excel to find Poisson probability

P(X = 10) = "=POISSON(10,9.5,0)" = 0.1235

The general command to find Poisson probability is as "=POISSON(x, , cumulative)"

Cumulative = 0 if we want to find exact probability.

cumulative = 1, if we want to find less than or equal ( <= ) that cumulative probability.

b) What is the probability of having less than three days of precipitation in the month of April?

P( X < 3) = P(X <= 2) = "=POISSON(2,9.5,1)" = 0.0042

c) What is the probability of having more than 15 days of precipitation in the month of April?

P(X > 15) = 1 - P(X <= 15) = "=1-POISSON(15,9.5,1)" = 0.0335