Question

A recruiting agent stated that, on average, 3.6 applicants fail to show up for their interview every week. What is the probability that exactly 6 applicants will not show up for their interview next week?

Analyze the given scenario and complete the following:

a. Determine which probability distribution should be used to model the scenario.

Hypergeometric

Geometric

Poisson

b. Calculate the probability of the indicated event.
P(x)=P(x)=

Round to 3 significant digits

c. Determine the expected value and variance of the random variable.
E(X)=E(X)=

Variance=Variance=

Answer 1

a)

Poisson

b)

Here, λ = 3.6 and x = 6
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 6)
P(X = 6) = 3.6^6 * e^-3.6/6!
P(X = 6) = 0.083
Ans: 0.083

c)

E(X)= 3.6

varaince = 3.6