Problem

Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $\$ 24,000$ and the standard deviation is $\$ 1000$. Use the 68-95-99.7 Rule to find the percentage of buyers who paid more than $\$ 27,000$. Price of a Model of a New Car (Thousands) The percentage of buyers who paid more than $\$ 27,000$ is $\%$.

Solution

Step 1 :The problem is asking for the percentage of buyers who paid more than $27,000 for a particular model of a new car. The prices paid for this car follow a normal distribution with a mean of $24,000 and a standard deviation of $1,000.

Step 2 :The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, almost all values lie within 3 standard deviations of the mean. More specifically, 68% of the data falls within the first standard deviation from the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.

Step 3 :In this case, a price of $27,000 is 3 standard deviations above the mean. According to the empirical rule, 99.7% of the data falls within three standard deviations of the mean.

Step 4 :This means that the percentage of buyers who paid more than $27,000, which is more than 3 standard deviations above the mean, is 100% - 99.7% = 0.3%.

Step 5 :Final Answer: The percentage of buyers who paid more than $27,000 is \(\boxed{0.3\%}\).

From Solvely APP
Source: https://solvelyapp.com/problems/G608bxdgZ4/

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