A bank manager sees an average of 5.4 new clients in her office every day. If the clients arrive at random throughout the day, determine the probability that she will see 4 clients in her office in the first half of the day today.

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=Round to 3 significant digits