The average number of acres burned by forest and range fires in a large New Mexico county is 4,300 acres per year, with a standard deviation of 700 acres. The distribution of the number of acres burned is normal. (a) What is the probability that between 2,00 and 4,200 acres will be burned in any given year?
Answers
Given : The average number of acres burned by forest and range fires in a large New Mexico county is 4,300 acres per year, with a standard deviation of 700 acres. Normal Distribution
To find : What is the probability that between 2,000 and 4,200 acres will be burned in any given year
Solution:
Mean = 4300
Standard Deviation SD = 700
Z score = ( Value - Mean) / SD
Z score for 2000 = (2000 - 4300)/700
= -2300/700
= -23/7
= -3.2857
Z score -3.29 is Equivalent to 0.0007
Z score for 4000 = (4200 - 4300)/700
= -100/700
= -1/7
= -0.143
Z score -0.143 is Equivalent to 0.443
Probability = 0.4430 - 0.0007
= 0.4423
0.4423 is the probability that between 2,000 and 4,200 acres will be burned in any given year
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