bmgf3m

2021-12-16

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?

Required:

What is the probability that at most eight policies are not terminated before maturity?

Ronnie Schechter

Beginner2021-12-17Added 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,$p=1-0.25=0.75$

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,

$P(X=x)=n{C}_{x}{p}^{x}{q}^{n-x}$

n number o samples

x number of success

p probability of success

q probability of failure

Step 2

to find the required probability:

$P(X\le 8)=\sum _{x=0}^{8}10{C}_{x}{\left(0.75\right)}^{x}{\left(0.25\right)}^{10-x}$

$=1-\sum _{x=9}^{10}10{C}_{x}{\left(0.75\right)}^{x}{\left(0.25\right)}^{10-x}$

$=1-[10{C}_{9}{\left(0.75\right)}^{9}{\left(0.25\right)}^{10-9}+10{C}_{10}{\left(0.25\right)}^{10-10}]$

$=1-[0.1877+0.0563]$

$=1-\left[0.2440\right]$

$=0.7560$

Therefore the probability that at most eight policies are not terminated before maturity is 0.7560 or 75.60%

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%

Then, the Probability of insurance not terminated before the maturity date is,

Assume that

Let success be the insurance not terminated before the maturity date the required calculation can be defined by the formula,

n number o samples

x number of success

p probability of success

q probability of failure

Step 2

to find the required probability:

Therefore the probability that at most eight policies are not terminated before maturity is 0.7560 or 75.60%

aquariump9

Beginner2021-12-18Added 40 answers

$p=0.25,q=1-p=1-0.25=0.75,n=10$

Let X be the number of policies terminated before maturity-

Probability that at most 8 policies and not terminated before maturity-

$P(X\le 8)=1-P\left(X>8\right)=1-[P(X=9)+P(X=10)]$

$=1-\left[{}^{\left\{10\right\}}{C}_{9}{\left(0.25\right)}^{9}{\left(0.75\right)}^{1}{+}^{10}{C}_{10}{\left(0.25\right)}^{10}\right]$

=1-(0.0000286+0.000009536)

$=1-0.00002955=0.999997$

nick1337

Expert2021-12-28Added 681 answers

An insurance company found that 25% of all insurance policies are terminated before their maturity date

Probability of policy not terminating

15 policies are randomly selected

probability that more than 8 but less than 11 policies are terminated before maturing

=0.0041

= 0.41% is the probability that more than 8 but less than 11 policies are terminated before maturing

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