A bank manager sees an average of 5.9 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)=

Round to 3 significant digits

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

Variance=

Round to 3 significant digits