Question

A consumer response team hears directly from consumers about the challenges they face in the​ marketplace, brings their concerns to the attention of financial​ institutions, and assists in addressing their complaints. The consumer response team accepts complaints related to​ mortgages, bank accounts and​ services, private student​ loans, other consumer​ loans, and credit reporting. An analysis of complaints over time indicates that the mean number of credit reporting complaints registered by consumers is

1.551.55

per day. Assume that the number of credit reporting complaints registered by consumers is distributed as a Poisson random variable. Complete parts​ (a) through​ (d) below.

a. What is the probability that on a given​ day, no credit reporting complaints will be registered by​ consumers?

The probability that no complaints will be registered is

nothing.

​(Round to four decimal places as​ needed.)

b. What is the probability that on a given​ day, exactly one credit reporting complaint will be registered by​ consumers?

The probability that exactly one complaint will be registered is

nothing.

​(Round to four decimal places as​ needed.)

c. What is the probability that on a given​ day, more than one credit reporting complaint will be registered by​ consumers?

The probability that more than one complaint will be registered is

nothing.

​(Round to four decimal places as​ needed.)

d. What is the probability that on a given​ day, fewer than two credit reporting complaints will be registered by​ consumers?

The probability that fewer than two complaints will be registered is

nothing.

​(Round to four decimal places as​ needed.)

Answer 1

Pmf of Poisson distribution is P(X=x) =

Where = 1.55 ( mean of Poisson variate)

P(X=x)= e^-1.55. (1.55)^x/x! = 0.2122 (1.55)^x/x!

A.The probability that no complaints will be registered is P(X=0)= 0.2122×(1.55)⁰/0!=0.2122

BThe probability that exactly one complaint will be registered is P(X=1)=0.2122×(1.55)¹/1!=.0.3289

C.The probability that more than one complaint will be registered is P(X>1)=1- P(X <=1)=1-[P(X=0)+P(X=1)]=1-(.2122+.3289)=0.4589

D.The probability that fewer than two complaints will be registered is P(X<2)=P(X=0)+P(X=1)=0.2122+0.3289= 0.5411