Question

April Showers bring May Flowers!! Research the "Average Amount of Days of Precipitation in April" for a city of your choice. According to Weather and Science Facts, The average number of days is 9 and 3.4 inches in Atlanta, Georgia. What is the probability of having exactly 10 days of precipitation in the month of April? The probability is 0.120 or 12.0% when rounded to one decimal. 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

Let X be the number of days of Precipitation in April.

Assuming that the number of days of Precipitation in April follows Poisson distribution, X ~ Poisson( = 9)

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

= exp(-9) * 9¹⁰ / 10! = 0.1186 0.12 = 12%

Probability of having less than three days of precipitation in the month of April = P(X < 3)

= P(X = 0) + P(X = 1) + P(X = 2)

= exp(-9) * 9⁰ / 0! + exp(-9) * 9¹ / 1! + exp(-9) * 9² / 2!

= 0.0001234098 + 0.0011106882 + 0.0049980971

= 0.0062

Using Normal approximation to Poisson distribution, the mean and variance is 9 days.

Probability of having more than 15 days of precipitation in the month of April = P(X > 15)

= P[z > (15 - 9) / 9]

= P[z > 0.67]

= 0.2525