Question

The average number of acres burned by all wildfires in the United States is 780 acres with standard deviation 500 acres. Of course, some wildfires burn thousands of acres, so the distribution of acres burned by wildfires is strongly right skewed. A random sample of wildfires is to be taken. Between which 2 values do 94% all sample means fall for samples of size 64? If you dont think the last answer is the correct answer, then choose the answer closest to the number you calculated.
a) between 608.1 and 9951.9 acres

b) between 662.5 and 897.5 acres

c) between 682.2 and 877.8 acres

d) between 657.5 and 902.5 acres

e) These values cannot be calculated because X is not normally distributed.

Answer 1

Answer:

option (b) between 662.5 and 897.5 acres

Step-by-step explanation:

Data provided in the question:

Average number of acres burned by all wildfires = 780 acres

Standard deviation, σ = 500 acres

sample size, n = 64

confidence level = 94% = 0.94

thus,

α = 1 - 0.94 = 0.06

Now,

$Z_{\frac{\alpha}{2}}=Z_{0.03}$ = 1.88  [from the standard Z table]

Therefore,

The lower limit = Mean - $\frac{\sigma\times Z}{\sqrt{n}}$

or

The lower limit = 780 - $\frac{\500\times1.88}{\sqrt{64}}$

or

The lower limit = 662.5 acres

and,

The upper limit = Mean + $\frac{\sigma\times Z}{\sqrt{n}}$

or

The upper limit = 780 + $\frac{\500\times1.88}{\sqrt{64}}$

or

The upper limit = 897.5 acres

Hence,

The correct answer is option (b) between 662.5 and 897.5 acres