According to the National Humane Society, "Stray Cost" or the cost of the care and feeding for a stray dog is $419.00 per year. This amount does not include veterinarian care, but only food, water and shelter. It was found that the standard deviation of this "Stray Cost" was $27.00. If the shape of the distrbution of these costs is unknown, approximately what percentage of straycosts would fall between $359 and $479 per year?

no

68

To determine the percentage of stray costs that would fall between $359 and $479 per year, we need to calculate the z-scores for these values.

Z-score can be calculated using the formula:
z = (X - μ) / σ

where X is the observed value, μ is the mean, and σ is the standard deviation.

Let's calculate the z-scores for $359 and $479 using the given information:

For $359:
z = ($359 - $419) / $27

For $479:
z = ($479 - $419) / $27

Using these z-scores, we can refer to the standard normal distribution table (also known as the z-table) to find the corresponding proportions.

However, since the shape of the distribution of stray costs is unknown, we don't have the exact z-score to refer to. In this case, we can use the empirical rule, also known as the 68-95-99.7 rule.

According to the empirical rule:

- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.

Since we don't know the exact shape of the distribution, we can make an approximation based on the empirical rule. We assume that the distribution is approximately normal.

If we assume the distribution is normal, we can estimate that approximately 68% of stray costs would fall within 1 standard deviation from the mean, 95% of stray costs would fall within 2 standard deviations from the mean, and 99.7% of stray costs would fall within 3 standard deviations from the mean.

Therefore, we can estimate that approximately 68% of stray costs would fall between $359 and $479 per year.