The number of snow days per winter at Windham High School is thought to be Poiss
ID: 3239465 • Letter: T
Question
The number of snow days per winter at Windham High School is thought to be Poisson distributed with a mean of 4.3 per year. What is the probability that: (Round to 4 decimal places.)
a. Fewer than 3 snow days will occur in a given year?
b. No snow days will occur in a given year?
c. 4 or 5 snow days occur in a given year?
d. Exactly 3 snow days will occur in a given year?
e. 5 or more snow days will occur in a given year?
f. What is the mean and standard deviation for the above Poisson distribution?
Explanation / Answer
= 4.3
P(X = x) = e- * x / x!
a) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= e-4.3 * 4.30 * 0! + e-4.3 * 4.31 * 1! + e-4.3 * 4.32 * 2!
= 0.1974
b) P(X = 0) = e-4.3 * 4.30 * 0! = 0.0136
c) P(X = 4 or 5) = P(X = 4) + P(X = 5)
= e-4.3 * 4.34 * 4! + e-4.3 * 4.35 * 5!
= 0.1933 + 0.1662
= 0.3595
d) P(X = 3) = e-4.3 * 4.33 * 3! = 0.1798
e) P(X > 5) = 1 - P(X < 5)
= 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)]
= 1 - [e-4.3 * 4.30 * 0! + e-4.3 * 4.31 * 1! + e-4.3 * 4.32 * 2! + e-4.3 * 4.33 * 3! + e-4.3 * 4.34 * 4! ]
= 1 - 0.5704
= 0.4296
f) mean = 4.3
standard deviation = 4.3