Answer:
Variance = 5
Standard deviation = 2.236
0.2650257
Step-by-step explanation:
For a Poisson distribution is σ² = μ.
Given that:
Mean , μ of bankruptcies files per hour = 5
μ = 5
For a Poisson distribution :
P(x = x) = (μ^x * e^-μ) / x!
The Variance and standard deviation :
Variance : σ² = μ = 5
Standard deviation = sqrt(variance) = sqrt(5) = 2.236
B.) Find the probability that at most three businesses will file bankruptcy in any given hour.
P( x ≤ 3) = P(0) + P(1) + P(2) + P(3)
P(x = 0) = (5^0 * e^-5) / 0! = 0.0067379
P(x = 1) = (5^1 * e^-5) / 1! = 0.0336897
P(x = 2) = (5^2 * e^-5) / 2! = 0.0842243
P(x = 3) = (5^3 * e^-5) / 3! = 0.1403738
0.0067379 + 0.0336897 + 0.0842243 + 0.1403738
= 0.2650257
