The average number of acres burned by forest and range fires in a county is 4,500 acres per year, with a standard deviation of 780 acres. The distribution of the number of acres burned is normal. What is the probability that between 3,000 and 4,800 acres will be burned in any given year? Round your answer to four decimal places.

0.6206

Step-by-step explanation:

We would be using the Z score probability to answer this question

The formula to find the is given as:

is z = (x-μ) / σ,

x = observed value

μ = mean or average value

σ = Standard deviation

To find the probability that between 3,000 and 4,800 acres will be burned in any given year

Step 1

Find the probability that that between 3,000 will be burned in any given year

z = (x-μ) / σ,

x = observed value = 3000

μ = mean or average value = 4500

σ = Standard deviation = 780

z = (3000 - 4500) / 780

z = - 1.92308

Step 2

Find the probability that that between 4,800 will be burned in any given year

z = (x-μ) / σ,

x = observed value = 4800

μ = mean or average value = 4500

σ = Standard deviation = 780

z = (4800 - 4500) / 780

z = 0.38462

Step 3

Using the Z score normal distribution table:

= P (Z <0.38462) - P (Z < - 1.92308)

= P (-1.92308 < Z < 0.38462)

Using the Z score normal distribution table:

P (z) - 1.92308 = 0.02743

P (z) 0.38462 = 0.64803

Therefore, the probability that between 3,000 and 4,800 acres will be burned in any given year

0.64803 - 0.02743

= 0.6206