Explanation Given Information: Acme Insurance company launching a drive and ensure racetrack drivers against wrecking the cars where a racetrack driver races 4 times in a year on an average and the chances of wrecking a vehicle is 1 out of 10 with worth of $ 100 , 000 in each race. When a driver is involved in an accident after paying for a new car, the company automatically drops the driver and not refund the premium which is $ 5 , 000 annual. Formula Used: When the number of trials is fixed and the outcomes of each trial are independent to each other, then the binomial random variable is used to count the number of successes in the sequence of independent Bernoulli trials. The expected value for X by use of the formula E ( X ) = ∑ i = 1 n x i ⋅ P ( X = x i ) . Calculation: Consider the insure racetrack drivers against wrecking the cars. Possible values of X include either profit or loss. If the car is wrecked by the driver, the amount of loss to the company. X = $ 5 , 000 − $ 1 , 00 , 000 X = − 95 , 000 If the car is not wrecked by the driver, the amount of profit to the company is $ 5 , 000 . X = 5 , 000 Evaluate the probability that car is wrecked in the first race, P ( W r e c k 1 ) = 1 10 = 0.1 Evaluate the probability that car is not wrecked in the first race, P ( N o W r e c k 1 ) = 1 − 0.1 = 0.9 Evaluate the probability that car is wrecked in the second race, if not wrecked in the first race. P ( W r e c k 2 ) = 0.1 Evaluate the probability that car is not wrecked in second race also, P ( N o W r e c k 2 ) = 1 − 0.1 = 0.9 Evaluate the probability that car is wrecked in the third race, if not wrecked previously. P ( W r e c k 3 ) = 0.1 Evaluate the probability that the car is not wrecked in the third race also, P ( N o W r e c k 3 ) = 1 − 0.1 = 0.9 Evaluate the probability that car is wrecked in the fourth race, if not wrecked previously. P ( W r e c k 4 ) = 0.1 Evaluate the probability that the car is not wrecked in the fourth race also, P ( N o W r e c k 4 ) = 1 − 0.1 = 0.9 The probability distribution is represented in a tree diagram. Evaluate the probability that the car is not wrecked by the driver in four races, P ( X = 5 , 000 ) P ( X = 5 , 000 ) = ( 0

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Question

Chapter 9.3, Problem 59E

To determine

To calculate: The expected amount of profit or loss by the Acme Insurance company to earn from a typical driver in a year while launching a drive and ensure racetrack drivers against wrecking the cars where a racetrack driver races 4 times in a year on an average and the chances of wrecking a vehicle is 1 out of 10 with worth of $100,000 in each race. When a driver is involved in an accident after paying for a new car, the company automatically drops the driver and not refund the premium which is $5,000 annual.

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Chapter 9 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - Prob. 2E Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - Prob. 5E Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - Prob. 7E Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - Prob. 16E Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - 2010 Income Distribution up to $100,000 The...Ch. 9.1 - 2003 Income Distribution up to $100,000 Repeat...Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Housing Prices Going into the Real Estate Bubble...Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Car Purchases To persuade his parents to...Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - 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Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - Prob. 17E Ch. 9.4 - Prob. 18E Ch. 9.4 - Prob. 19E Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - Prob. 21E Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - Prob. 25E Ch. 9.4 - Prob. 26E Ch. 9.4 - Unemployment Following is a sample of unemployment...Ch. 9.4 - Prob. 28E Ch. 9.4 - Prob. 29E Ch. 9.4 - Prob. 30E Ch. 9.4 - Prob. 31E Ch. 9.4 - Prob. 32E Ch. 9.4 - Prob. 33E Ch. 9.4 - Prob. 34E Ch. 9.4 - 2010 Income Distribution up to $100,000 The...Ch. 9.4 - Prob. 36E Ch. 9.4 - Hispanic Employment: Male The following table...Ch. 9.4 - Prob. 38E Ch. 9.4 - Prob. 39E Ch. 9.4 - Prob. 40E Ch. 9.4 - Prob. 41E Ch. 9.4 - Prob. 42E Ch. 9.4 - Prob. 43E Ch. 9.4 - Prob. 44E Ch. 9.4 - Prob. 45E Ch. 9.4 - Prob. 46E Ch. 9.4 - Prob. 47E Ch. 9.4 - Prob. 48E Ch. 9.4 - Prob. 49E Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Prob. 51E Ch. 9.4 - Prob. 52E Ch. 9.4 - Prob. 53E Ch. 9.4 - Prob. 54E Ch. 9.4 - Prob. 55E Ch. 9.4 - Prob. 56E Ch. 9.4 - Prob. 57E Ch. 9.4 - Prob. 58E Ch. 9.4 - Prob. 59E Ch. 9.4 - Prob. 60E Ch. 9.4 - Prob. 61E Ch. 9.4 - Prob. 62E Ch. 9.4 - Prob. 63E Ch. 9.4 - Prob. 64E Ch. 9.4 - Prob. 65E Ch. 9.4 - Prob. 66E Ch. 9.4 - Prob. 67E Ch. 9.4 - Prob. 68E Ch. 9.4 - Prob. 69E Ch. 9.4 - Prob. 70E Ch. 9.4 - Prob. 71E Ch. 9.4 - Prob. 72E Ch. 9.4 - Prob. 73E Ch. 9.4 - Prob. 74E Ch. 9.4 - Prob. 75E Ch. 9.4 - Prob. 76E Ch. 9.4 - Prob. 77E Ch. 9.4 - Prob. 78E Ch. 9.4 - Prob. 79E Ch. 9.4 - Prob. 80E Ch. 9.5 - Prob. 1E Ch. 9.5 - Prob. 2E Ch. 9.5 - Prob. 3E Ch. 9.5 - Prob. 4E Ch. 9.5 - Prob. 5E Ch. 9.5 - Prob. 6E Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - Prob. 9E Ch. 9.5 - Prob. 10E Ch. 9.5 - Prob. 11E Ch. 9.5 - Prob. 12E Ch. 9.5 - Prob. 13E Ch. 9.5 - Prob. 14E Ch. 9.5 - Prob. 15E Ch. 9.5 - Prob. 16E Ch. 9.5 - Prob. 17E Ch. 9.5 - Prob. 18E Ch. 9.5 - Prob. 19E Ch. 9.5 - Prob. 20E Ch. 9.5 - Prob. 21E Ch. 9.5 - Prob. 22E Ch. 9.5 - Prob. 23E Ch. 9.5 - Prob. 24E Ch. 9.5 - Prob. 25E Ch. 9.5 - Prob. 26E Ch. 9.5 - SAT Scores SAT test scores are normally...Ch. 9.5 - Prob. 28E Ch. 9.5 - Prob. 29E Ch. 9.5 - Prob. 30E Ch. 9.5 - IQ Scores IQ scores (as measured by the...Ch. 9.5 - Prob. 32E Ch. 9.5 - Prob. 33E Ch. 9.5 - Prob. 34E Ch. 9.5 - Prob. 35E Ch. 9.5 - Prob. 36E Ch. 9.5 - Baseball The mean batting average in major league...Ch. 9.5 - Prob. 38E Ch. 9.5 - Marketing Your pickle company rates its pickles on...Ch. 9.5 - Prob. 40E Ch. 9.5 - Prob. 41E Ch. 9.5 - Prob. 42E Ch. 9.5 - Prob. 43E Ch. 9.5 - Prob. 44E Ch. 9.5 - Prob. 45E Ch. 9.5 - Prob. 46E Ch. 9.5 - Prob. 47E Ch. 9.5 - Prob. 48E Ch. 9.5 - Prob. 49E Ch. 9.5 - Prob. 50E Ch. 9.5 - Prob. 51E Ch. 9.5 - Prob. 52E Ch. 9.5 - Prob. 53E Ch. 9.5 - Prob. 54E Ch. 9.5 - Prob. 55E Ch. 9.5 - Prob. 56E Ch. 9.5 - Prob. 57E Ch. 9.5 - 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Solution Summary: The author calculates the expected amount of profit or loss by Acme Insurance company to earn from a typical driver.

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Chapter 9 Solutions