An insurance company found that 25% of all insurance policies

bmgf3m 2021-12-16 Answered
An insurance company found that 25% of all insurance policies are terminated before their maturity date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a Binomial experiment.
Required:
What is the probability that at most eight policies are not terminated before maturity?
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Expert Answer

Ronnie Schechter
Answered 2021-12-17 Author has 27 answers
Step 1
Given,
An insurance company found that all insurance policies terminated before their maturity date.
The Probability of insurance terminated before the maturity date is 25%
q=0.25
Then, the Probability of insurance not terminated before the maturity date is, p=10.25=0.75
Assume that n=10 policies are randomly selected from the company’s policy database.
Let success be the insurance not terminated before the maturity date the required calculation can be defined by the formula,
P(X=x)=nCxpxqnx
n number o samples
x number of success
p probability of success
q probability of failure
Step 2
to find the required probability:
P(X8)=x=0810Cx(0.75)x(0.25)10x
=1x=91010Cx(0.75)x(0.25)10x
=1[10C9(0.75)9(0.25)109+10C10(0.25)1010]
=1[0.1877+0.0563]
=1[0.2440]
=0.7560
Therefore the probability that at most eight policies are not terminated before maturity is 0.7560 or 75.60%
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aquariump9
Answered 2021-12-18 Author has 40 answers
p=0.25,q=1p=10.25=0.75,n=10
Let X be the number of policies terminated before maturity-
Probability that at most 8 policies and not terminated before maturity-
P(X8)=1P(X>8)=1[P(X=9)+P(X=10)]
=1[{10}C9(0.25)9(0.75)1+10C10(0.25)10]
PSK=1-(0.0000286+0.000009536)
=10.00002955=0.999997
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nick1337
Answered 2021-12-28 Author has 510 answers

An insurance company found that 25% of all insurance policies are terminated before their maturity date
Probability  of  policy termination p=25100=14
Probability of policy not terminating  =11/4=3/4
15 policies are randomly selected n=15
p(x)=nCxpxqnx
probability that more than 8 but less than 11 policies are terminated before maturing
x=9,10
probability=p(9)+p(10)
=15C9(14)9(34)6+15C10(14)10(34)5
=(35/415)(50053+3003)
=(35/415)(18018)
=0.0041 
= 0.41% is the probability that more than 8 but less than 11 policies are terminated before maturing

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