   Chapter 8.5, Problem 31E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In the following problems use a normal approximation to the binomial.Insurance Empirical records show that the probability is 0.06 that a driver insured with Riders Insurance Company will have an accident during 2016 in which he or she is at fault. If the company has 12,000 drivers insured in Century City, what is the probability that at most 800 will have an at-fault accident in 2016?

To determine

To calculate: The probability that maximum 800 will have an at fault accident in 2016 if practical data show that the probability is 0.06 for a driver insured with Riders Insurance company will have an accident in the year 2016 in which he or she is at fault.

Explanation

Given Information:

The practical data show that the probability is 0.06 that a driver insured with Riders Insurance company will have an accident in the year 2016 in which he or she is at fault.

Formula used:

If data for a population are normally distributed and σ is the standard deviation of the population data, then the number of standard deviations that x is from the mean μ is given by the z-score as;

z=xμσ

If n is the number of times the events are repeated and p is probability then mean is;

μ=np

And standard deviation is;

σ=npq

Calculation:

Consider that the insurance and it is a binomial experiment with,

n=12,000p=0.06

The probability that at most 800 will have an accident in the year 2016 so;

Pr(x800.5)

Where n is the number of drivers insured in the city.

And p is the probability that the driver insured with rider’s insurance that is the chance to win.

Now find the value of μ(mean) as;

μ=np=12,000×0.06=720

Where q is the probability to lose and calculated as;

q=1p=10

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