Question

The average number of acres burned by forest and range fires in a large Zambian province (North-Western) is 4300 acres per year, with a standard deviation of 750 acres. The distribution of the number of acres burned is normal. What is the probability that between 2500 and 4200 acres will be burned in any given year?

Answer 1

The probability that between 2500 and 4200 acres will be burned in any given year is 0.4633 (or 46.33%).

Step-by-step explanation:

To find the probability that between 2500 and 4200 acres will be burned in any given year, we need to calculate the z-scores for these values using the formula:

z = (x - μ) / σ

Where x is the value, μ is the mean, and σ is the standard deviation.

For 2500 acres:

z = (2500 - 4300) / 750 = -2.267

For 4200 acres:

z = (4200 - 4300) / 750 = -0.133

Next, we need to find the area between these two z-scores on a standard normal distribution table. This represents the probability.

Using a standard normal distribution table, the area between -2.267 and -0.133 is approximately 0.4633.

Therefore, the probability that between 2500 and 4200 acres will be burned in any given year is 0.4633 (or 46.33%).