The average number of acres of forest burned by a range fire

The average number of acres of forest burned by a range fire in a large Wyoming county is 4300 acres per year, with a standard deviation of 750 acres. The distribution of the number of acres burned is normally distributed

Question

Answer

What is the probability that more than 5,000 acres will be burned in a year?

What is the probability that fewer than 4,000 acres will be burned in a year?

What is the probability that between 2,500 and 4,200 acres will be burned?

In those years where more than 5,500 acres are burned, help is needed from eastern-region fire teams. Determine the probably that help will be needed in a given year.

Solution

a)

z = (X -Mean)/SD

Z(X>5000) = (5000 - 4300)/750 = 0.93

P(X>5000) = 1 - 0.8238 = 0.1762 Answer

b)

z = (X -Mean)/SD

Z(X<4000) = (4000 - 4300)/750 = -0.4

P(X>5000) = 0.3446 Answer

c)

z = (X -Mean)/SD

Z(2500<X<4200) = (2500 - 4300)/750 < z < (4200 - 4300)/750

= -2.4 < z < -0.13

P(2500<X<4200) = 0.4483 - 0.0082 = 0.4401 Answer

d)

z = (X -Mean)/SD

Z(X>5500) = (5500 - 4300)/750 = 1.6

P(X>5500) = 1 - 0.9452 = 0.0548 Answer