Hello, Can you help me out with this Statistics and Data Analysis Questions. Thank you for your help in advance.

Problem 1

A certain region is known to be plagued by forest fires. One state district notes the average area that is burned 3200 acres per year with a standard deviation of 620 acres.

1. In one to two paragraphs, and in your own words, describe what is meant by standard deviation. Note: I do not want a mathematical explanation. Rather, I want you to explain in words what the standard deviation is. You can include numbers if you need them to help with your discussion, but I do not want to see the actual formula for SD. This question is worth up to 3 points. You will be given full points based on your ability to convince the grader that you do indeed understand the concept of SD. Note: You may be asked to do do this again on one of your exams....

2. What is meant by a percentile?

3. What is the probability of having an area of less than 2700 acres burned in a given year?

4. If exactly 3000 acres were burned, what percentile would this correspond to?

5. How many acres would be burned to be in the 75th percentile?

6. What percentage of years would see a burn between would score between 2500 and 3000?

7. What percentage of years will have a z-score below -1.3?

8. What percentage of years will have a z-score greater than -0.8?

Problem #2

In an adjacent county, the following values of forest fire destruction (in acres) were recorded over a series of time:

3518, 2786, 3143, 2140, 3063, 2067, 3251, 4188, 3150, 3842, 3021, 2908, 3143, 2763, 3730, 2770, 2681, 2911, 2954, 2902, 1728, 2559, 3985, 1267, 3472, 3037, 2353, 2551, 2829, 3519, 3306, 2096, 2959, 3780, 2253, 1998, 3679, 3322, 2593, 4509, 3563, 4216, 3239, 3693, 3489, 3183, 5045, 3125, 2332, 2473, 4853, 3495, 3436, 2554, 2833, 2875, 1931, 1921, 2564, 2400, 2808, 2967, 2587, 2249, 4506, 4369, 3122, 3225, 2728, 4353

Using R (as well as your mind!), answer the following:

1. Draw a histogram.

2. Then describe the distribution of this variable. (Hint: Review in your notes/resources for this course what is some key information needed to properly describe a distribution.)

3. There is another graph we can use to help confirm that the variable is normally distributed. Plot this graph and describe what this graph tells us. Then indicate whether or not you would say that this variable is normally distributed.

4. Draw a boxplot. What does an open circle represent? What do you want to do with any such observation(s) in this dataset? Would you remove any of them?

Problem #3

You must use the empirical rule to answer the problems in this question. In other words, I do not want you to use Rs pnorm() function to answer any of these questions.

Data from the rainfall in the western region of Scotland (in inches) was approximately normally distributed with: N(180.2, 3.8)

1. One year resulted in 187.8 inches. What percentile does this correspond to?

2. What percentage of years had between 176.4 and 187.8 inches?

3. If an item is manufactured with a z-score of +4, how much rain would this correpond to?

4. Do not use the empirical rule for this problem. Instead, use R for a precise calculation. One year was in the 97th percentile. How much rain does that correspond to? Hint: There is an R function that will give you this exact piece of information. That is, it converts the area under the normal density curve back into a z-score.