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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Hello I am being asked to find the probability that a policy costs more than $1750 to have my answer right.

A study by Quadrant Information Services commissioned by Insure.com calculated auto insurance rates for each of the 50 states; and as a result, the average annual rate for the United States was $1,317. Suppose annual rates of auto insurance in the United States are normally distributed with a standard deviation of $324.

According to MoneyGeek, a state minimum auto insurance policy in Florida costs an average of $1123 pe

Answwe: What is the probability that a randomly selected auto insurance rate in the United States would be greater than $1,750?

Value standardization is required using the following formula below in order to determine the likelihood that a car insurance rate chosen at random in the United States would be higher than $1,750:

z = (x - mu) / sigma

mu is the mean of the distribution, x is the interest value, and sigma is the standard deviation. Substituting the given values,

z = (1750 - 1317) / 324 = 1.34

We can calculate the probability of selecting an auto insurance rate above $1,750 by finding the probability of z being greater than 1.34 using a standard normal table or calculator. The result is approximately 9.01%, which means that there is a 9.01% chance of selecting an auto insurance rate above $1,750 from a random sample in the United States. This result is not unexpected, considering that $1,750 is higher than the mean and one standard deviation, suggesting that it is a relatively high value.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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