d Nick is an insurance agent He expects to receive 5 claims

d Nick is an insurance agent He expects to receive 5 claims a month from his customers. Assuming 4 weeks in a month, what is the probability he receives no Claims in a week? e. Lucy is an auditor for Nick?s insurance company. Each year she randomly selects 10 of Nick?s claims handled that year to look for mistakes. This year Nick handled 60 claims and made mistakes on 3 of them What is the probability Lucy selects 1 of Nick?s mistakes in here sample? What is the probability that 10 randomly selected students have GPAs above 35, if the probability of a GPA above 3.5 is 0.08?

Solution

Answer

The variable is a Poisson with average 5 per month.

For a week average = 1.25

d) P(x=0) = 0.2865

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e) X is the no of mistakes found.

X is a binomial variate with p = 3/60 = 0.05

n=10

P(X=1) = 10C1*0,05)(0,95)⁹

=0.3151

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f) p =3.5 and n =10

Mean = 35

Prob for 10 student having GPA >3,5

= (0,8)¹⁰ (as each boy gpa is independent.)