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igomit [66]
3 years ago
7

An automotive insurance company has 30,000 policyholders, and the accident rate is 0.06. If the company needs to make a profit o

f $1,740,000 this year and the payout for each claim (after deductibles) is $8,200, the minimum premium it must charge is
Mathematics
1 answer:
bogdanovich [222]3 years ago
7 0
Number of accidents = number of policyholders * accident rate = 30,000 * 0.06 = 1,800

Total payout = payout per each claim * number of claims

Number of claims = number of accidents

=> Total payout = $8,200 * 1,800 =   $ 14,760,000

Total minimum premium = total payout + profit = $ 14,760,000 + $ 1,740,000 = $ 16,500,000.

Minimum premum charge = total minimum premum / number of policyholders

Minimum premium charge = $ 16,500,000 / 30,000 =  $550

Answer: $ 550
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Answer:

0.0011 = 0.11% probability of selling less than 3 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A real estate agent has 17 properties that she shows.

This means that n = 17

She feels that there is a 50% chance of selling any one property during a week.

This means that p = 0.5

Compute the probability of selling less than 3 properties in one week.

This is

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0.0001 + 0.0010 = 0.0011

0.0011 = 0.11% probability of selling less than 3 properties in one week.

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