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Statistics and Probability

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1) Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22.
a.Compute the mean number and median number of apples in a bag.
b.Verify that S (X - X) = 0.

2) The Citizens Banking Company is studying the number of times the ATM located in a Loblaws Supermarket at the foot of Market Street is used per day. Following are the numbers of times the machine was used over each of the last 30 days. Determine the mean number of times the machine was used per day.
83 64 84 76 84 54 75 59 70 61
63 80 84 73 68 52 65 90 52 77
95 36 78 61 59 84 95 47 87 60

3)The American Automobile Association checks the prices of gasoline before many holiday weekends. Listed below are the self-service prices for a sample of 15 retail outlets during the May 2003 Memorial Day weekend in the Detroit, Michigan, area.
1.44 1.42 1.35 1.39 1.49 1.49 1.41 1.46
1.41 1.49 1.45 1.48 1.39 1.46 1.44
What is the arithmetic mean selling price?
What is the median selling price?
What is the modal selling price?

4) A recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3 percent per year, you'll need to make $33,598 in 10 years to have the same buying power. You would need to make $44,771 if the inflation rate jumped to 6 percent. Confirm that these statements are accurate by finding the geometric mean rate of increase.

5) The weights (in pounds) of a sample of five boxes being sent by UPS are: 12, 6, 7, 3, and 10.
Compute the range.
Compute the mean deviation.
Compute the standard deviation.

6) A sample of 2,000 licensed drivers revealed the following number of speeding violations.
Number of Violations Number of Drivers
0 1,910
1 46
2 18
3 12
4 9
5 or more 5
Total 2,000

What is the experiment?
List one possible event.
What is the probability that a particular driver had exactly two speeding violations?
What concept of probability does this illustrate?

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Solution Summary

This is a problem set with 6 questions involving descriptive statistics (mean, median, mode, geometric mean, range, and standard deviation) and probability.

Solution Preview

See the attached file for the same text.

1) Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22.

a.Compute the mean number and median number of apples in a bag.

To compute the mean number (i.e. the average), add the number of apples together (to get 152) and divide by the number of bags (7):

Mean = 152/7 = 21.7

To compute the median, sort the numbers from lowest to highest, and pick the number in the middle of the list (the 4th number):

Median = 22

b.Verify that S (X - X) = 0.

I figured out that this means the sum of each number minus the mean.

(23-21.7) + (19-21.7) + ... + 22 + 21.7
= 1.286 - 2.714 + 4.286 - 4.714 - 0.714 + 2.286 + 0.286
= 0

2) The Citizens Banking Company is studying the number of times the ATM located in a Loblaws Supermarket at the foot of Market Street is used per day. Following are the numbers of times the machine was used over each of the last 30 days. Determine the mean number of times the machine was used per day.
83 64 84 76 84 54 75 59 70 61
63 80 84 73 68 52 65 90 52 77
95 36 78 61 59 84 95 47 87 60

Again, the mean is the total (all the numbers added together) divided by the number of observations (30):

Mean = 2116/30 = 70.533

3)The American Automobile Association checks the prices of gasoline before many holiday weekends. Listed below are the self-service prices for a sample of 15 retail outlets during the May 2003 Memorial Day weekend in the Detroit, Michigan, area.
1.44 1.42 1.35 1.39 1.49 1.49 1.41 1.46
1.41 1.49 1.45 1.48 1.39 1.46 1.44

What is the arithmetic mean selling price?

The "arithmetic mean" is just another term for the mean, or the average:
Mean = 21.570/15 = 1.438

What is the median selling price?

Again, sort the numbers, and take the number in the middle (note, ...

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