Question

The distribution of number of acres burned by forest and range fires in a large New Mexico County is approximately normal with mean = 4300 acres per year, and standard deviation = 750 acres.

How many acres will have to be burned this year for it to be in the 25th percentile? Round answer to the nearest whole acre. Show your work: Shade and label the normal curve and state which function you used on the calculator

Answer 1

To find the number of acres that will have to be burned this year for it to be in the 25th percentile, we need to calculate the z-score for the 25th percentile using the standard normal distribution table or a calculator. Then, we can use the z-score to find the corresponding value using the formula x = (z * standard deviation) + mean.

Step-by-step explanation:

To find the number of acres that will have to be burned this year for it to be in the 25th percentile, we need to find the z-score corresponding to the 25th percentile and then use that z-score to find the corresponding value. The z-score formula is z = (x - mean) / standard deviation. Rearranging the formula to solve for x, we have x = (z * standard deviation) + mean. We can calculate the z-score using the standard normal distribution table or a calculator.

To calculate the z-score using a calculator, we can use the formula z = invNorm(0.25), where invNorm is the inverse normal function. Using this formula, we find that z = -0.674, rounding to three decimal places.

Now we can substitute the values into the formula x = (z * standard deviation) + mean. Plugging in the values, we have x = (-0.674 * 750) + 4300 = 4002.05 acres. Rounding to the nearest whole acre, we get 4002 acres.