Calculus and Above

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1. Please show all of your work when answering the following:

I. Use Chebyshev’s theorem to find what percent of the values will fall between 166 and 346 for a data set with a mean of 256 and standard deviation of 18.

II. Use the Empirical Rule to find what two values 95% of the data will fall between for a data set with a mean of 272 and standard deviation of 14.

2. Nine college students had eaten the following number of times at a fast food restaurant for dinner in the last ten days:

8, 0, 7, 1, 2, 3, 3, 8, 1

Find the mean, median, mode, range, and midrange for these data. Please show all of your work.

3. A Math test has a mean of 40 and standard deviation of 17.0. Find the corresponding z scores for:

I. a test score of 35

II. a test score of 95

Please show all of your work.

4. Rank the following data in increasing order and find the position and value of the 28th percentile. Please show all of your work.

4 2 7 4 2 5 6 4 4 0 0 1

5. The following data lists the average monthly snowfall for January in 15 cities around the US:

26 6 5 45 44 10 39 33

15 33 11 36 36 4 32

Find the mean, variance, and standard deviation. Please show all of your work.

6. Starting with the data values 70 and 100, add three data values to the sample so that the mean is 77, the median is 72, and the mode is 72. Please show all of your work.

I. Use Chebyshev’s theorem to find what percent of the values will fall between 166 and 346 for a data set with a mean of 256 and standard deviation of 18.

II. Use the Empirical Rule to find what two values 95% of the data will fall between for a data set with a mean of 272 and standard deviation of 14.

2. Nine college students had eaten the following number of times at a fast food restaurant for dinner in the last ten days:

8, 0, 7, 1, 2, 3, 3, 8, 1

Find the mean, median, mode, range, and midrange for these data. Please show all of your work.

3. A Math test has a mean of 40 and standard deviation of 17.0. Find the corresponding z scores for:

I. a test score of 35

II. a test score of 95

Please show all of your work.

4. Rank the following data in increasing order and find the position and value of the 28th percentile. Please show all of your work.

4 2 7 4 2 5 6 4 4 0 0 1

5. The following data lists the average monthly snowfall for January in 15 cities around the US:

26 6 5 45 44 10 39 33

15 33 11 36 36 4 32

Find the mean, variance, and standard deviation. Please show all of your work.

6. Starting with the data values 70 and 100, add three data values to the sample so that the mean is 77, the median is 72, and the mode is 72. Please show all of your work.

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