Question

More than 50 million guests stay at bed and breakfasts (B&Bs) each year. The website for the Bed and Breakfast Inns of North America, which averages three visitors per minute, enables many B&Bs to attract guests. Round your answers to four decimal places. a. Compute the probability of no website visitors in a one-minute period. b. Compute the probability of two or more website visitors in a one-minute period. c. Compute the probability of one or more website visitors in a 30-second period d. Compute the probability of four or more website visitors in a one-minute period

Answer 1

a)

Here, λ = 3 and x = 0
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 0)
P(X = 0) = 3^0 * e^-3/0!
P(X = 0) = 0.0498
Ans: 0.0498

b)

Here, λ = 3 and x = 2
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > =2) = 1 - P(X <= 1).
P(X > =2) = 1 - (3^0 * e^-3/0!) + (3^1 * e^-3/1!)
P(X > = 2) = 1 - (0.0498 + 0.1494)
P(X > =2) = 1 - 0.1992 = 0.8008

c)

Here, λ = 1.5 and x = 1
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > =1) = 1 - P(X <= 0).
P(X > =1) = 1 - (1.5^0 * e^-1.5/0!)
P(X > =1) = 1 - (0.2231)
P(X > =1) = 1 - 0.2231 = 0.7769

d)

Here, λ = 3 and x = 4
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > =4) = 1 - P(X <= 3).
P(X > =4) = 1 - (3^0 * e^-3/0!) + (3^1 * e^-3/1!) + (3^2 * e^-3/2!) + (3^3 * e^-3/3!)
P(X > =4) = 1 - (0.0498 + 0.1494 + 0.224 + 0.224)
P(X > =4) = 1 - 0.6472 = 0.3528