Question

13. The ages of cars owned by all people living in a city have a mean of 7.3 years and standard deviation of 2.2 years. Using the empirical rule, find the percentage of cars in the city that are between 5.1 and 9.5 years old.

Answer 1

Answer 2

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that applies to normal distributions. It states that:

1. Approximately 68% of the data falls within one standard deviation of the mean.

2. Approximately 95% of the data falls within two standard deviations of the mean.

3. Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, we have the mean of car ages as 7.3 years and a standard deviation of 2.2 years.

Step 1: Calculate the range within one standard deviation from the mean: Lower bound = Mean - Standard deviation Lower bound = 7.3 - 2.2 = 5.1 years

Upper bound = Mean + Standard deviation Upper bound = 7.3 + 2.2 = 9.5 years

Step 2: Find the percentage of data that falls within this range (between 5.1 and 9.5 years).

We know that approximately 68% of the data falls within one standard deviation of the mean. So, the percentage of cars between 5.1 and 9.5 years old is also approximately 68%.

Thus, the percentage of cars in the city that are between 5.1 and 9.5 years old is approximately 68%.