Question

Assume that X is a Poisson random variable with μ = 28. Calculate the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

a.	P(X ≤ 16)
b.	P(X = 20)
c.	P(X > 23)
d.	P(25 ≤ X ≤ 34)

Answer 1

Solution :

Given that mean μ = 28

=> For poisson distribution , P(x , μ) = (e^(-μ) * μ^x)/x!

a. => P(x <= 16) = 1 - P(x > 16)

= 1 - 0.9899

= 0.0101

b. => P(x = 20) = (e^(-28) * 28^20)/20!

= 0.0249

c. => p(x > 23) = 1 - P(x <= 23)

= 1 - 0.1998

= 0.8002

d.

=> P(25 <= x <= 34) = 0.6280

= P(x = 25) + P(x = 26) + P(x = 27) + P(x = 28) + P(x = 29) + P(x = 30) + P(x = 31) + P(x = 32) + P(x = 33) + P(x = 34)

= (e^(-28) * 28^25)/25! + (e^(-28) * 28^26)/26! + (e^(-28) * 28^27)/27! + (e^(-28) * 28^28)/28! + (e^(-28) * 28^29)/29! + (e^(-28) * 28^30)/30! + (e^(-28) * 28^31)/31! + (e^(-28) * 28^32)/32! + (e^(-28) * 28^33)/33! + (e^(-28) * 28^34)/34!

= 0.0673 + 0.0725 + 0.0752 + 0.0752 + 0.0726 + 0.0677 + 0.0612 + 0.0535 + 0.0454 + 0.0374

= 0.6280