Question

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.

Answer 1

Answer: 0.6225

Explanation:

$P\left(3,000<X<4,800\right)=0.6225

The mean is μ=4500 and the standard deviation is σ=780. Because the probability between two values is to be calculated, subtract the probability of the lower value from the higher value. In this case, you have to use the NORMDIST function twice.

1. Open Excel and click on any empty cell. Click Insert function, fx.

2. Search for NORMDIST in the search for a function dialog box and click GO.

3. Make sure NORMDIST is on top in select a function. Then click OK.

4. In the function arguments of the NORMDIST function, enter 4800 for X, 4500 for mean, 780 for Standard_dev, and TRUE for Cumulative, all for the higher value of X. Thus, the answer, rounded to four decimal places, is 0.6497.

5. Click on any other empty cell. Click Insert function, fx.

6. Search for NORMDIST in the search for a function dialog box and click GO.

7. Make sure NORMDIST is on top in select a function. Then click OK.

8. In the function arguments of the NORMDIST function, enter 3000 for X, 4500 for mean, 780 for Standard_dev, and TRUE for Cumulative, all for the lower value of X. Thus, the answer, rounded to four decimal places, is 0.0272.

Now subtract: 0.6497−0.0272=0.6225. Thus, the probability that between 3,000 and 4,800 acres will be burned in any given year is 0.6225.

Answer 2

0.6206

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