A consumer response team hears directly from consumers about the challenges they

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 1.95 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?

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

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

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

Explanation / Answer

This is a Poisson Process.

Note that,

P(x) = u^x e^(-u)/x!

where x = number of successes
u = mean = 1.95.

a)

Plugging in x = 0,

P(0) = 0.142274072 [answer]

******

b)

Plugging in x= 1,

P(1) = 0.27743444 [answer]

*********

c)

P(more than 1) = 1 - [P(0) + P(1)] = 0.580291489 [answer]

***********

d)

P(fewer than 2) = P(0) + P(1) = 0.419708511 [answer]

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