A study by Quadrant Information Services commissioned by insure.com calculated a

Question

A study by Quadrant Information Services commissioned by insure.com calculated auto insurance rates for each of 50 states; and as a result, the average annual rate for the United States was $1317.Suppose annual rates of auto insurance in the United States are normally distributed with a standard deviation of #324. Based on these data, what is the probability that a randomly selected auto insurance rate in the United States would be greater than $1750? what percentage of auto insurance rates would be less than $1200? What percentage of auto insurance rates would be between $1100 and $1500?

Explanation / Answer

Mean (M) = 1317

standard deviation (s) = 324

insurance rate above 1750

a= 1750

we find the z-score for the given values and then use that z-score in standard normal distribution tables to find probability.

z = (a-M)/s

z = (1750-1317)/324

z = 1.34

using the standard normal distribution tables p = 0.9099

but this is the probability of insurance values below 1750.

Hence above 1750 p = 1-0.9099 = 0.901

less than 1200:

a = 1200

z = (1200 - 1317)/324

z = -0.36

p = 0.3594

Hence, probability of insurace rates being less that 1200 is 0.3594

between 1100 and 1500.

Here we find the probablity of rates being less than both 1100 and 1500.

less than 1100:

z = (1100 - 1317)/324

z = -0.67

p for less than 1100 is = 0.2514

similarly less than 1500

z = (1500 - 1317)/324

z = 0.57

p for less than 1500 is = 0.7157

probability of between 1100 and 1500 = 0.7157 - 0.2514 = 0.4643

Hence, rates would be between 1100 and 1500 with probability 04643

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