Question

1. A)

Suppose that incoming calls per hour to an agent of a customer service center of a small credit union are uniformly distributed between 0 and 6 calls. If the center has 10 independent agents, what is the probability that exactly 5 agents receive between 2 and 5 calls?

0.2461

0.2051

0.6230

0.5

0

B)

Suppose that incoming calls per hour to an agent of a customer service center of a small credit union are uniformly distributed between 0 and 6 calls. If the center has 10 independent agents, what is the standard deviation of the number of agents who receive between 2 and 5 calls?

2.5

1.58

1.73

None of the answers

Answer 1

Ans:

Probability of getting between 2 and 5 calls

=(5-2)/(6-0)

=3/6

=0.5

a)Let y be the number of agents who gets calls between 2 and 5 calls.

Use binomial distribution with 10 and p=0.5

P(y=5)=10C₅*0.5^5*(1-0.5)^5=0.2461

b)

standard deviation of the number of agents who receive between 2 and 5 calls

=sqrt(10*0.5*0.5)

=1.58