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Exercises



Exercises for Sections  3.1-  3.5

1.
Consider the following data:
1.2, 2.6, 3.5, 2.2, 1.4, 1.9, 4.4, 1.8, 3.8
Calculate the
(a)
average
(b)
SD
(c)
median
(d)
range

2.
The typical American generates about 3.8 pounds of solid trash per day with standard deviation of 1.5 pounds. Assuming that the histogram for trash produced per day is approximately bell-shaped, between what two values will 95% of the observations fall?

3.
The following data are the monthly rental prices (in dollars) for a sample of 15 unfurnished 2-bedroom apartments off-campus.
675, 550, 650, 750, 575, 600, 560, 775, 850, 725, 625, 700, 740, 1100, 625
(a)
Calculate the average, median, SD and range.
(b)
Obtain a histogram and boxplot with your TI-83. What is the shape?
(c)
Based on the information you've gathered so far, how would you answer the question ``How much should I expect to pay for an unfurnished 2-bedroom apartment off-campus?''.
(d)
If you are to choose between the average and median, which do you think is a better measure of location for this data set? Why?

4.
Consider the following histogram. Suppose 95% of the data falls between 12.4 and 46.8. Using the empirical rule, give an estimate of the standard deviation for this sample of data.

\epsfig{file=histexcel.eps, height=3.5in}

5.
Consider the following sample of data:
11.2, 28.4, 32.6, 17.0, 13.5, 2.2, 38.0, 41.4, 1.9, 14.4, 21.8, 23.8
(a)
Calculate the quartiles.
(b)
Calculate the average
(c)
Calculate the standard deviation.

Exercises for Sections  3.63.7

6.
A random sample of 10 different unfurnished 1-bedroom apartments off-campus yield an average monthly rent of $500 with SD $100. A second sample of 10 2-bedroom apartments yield an average rent of $650 with SD $100.

(a)
Suppose that WMU students get a $20 discount on the monthly rent for all 1-bedroom apartments. The discounted monthly rent for the sample of 1-bedroom apartments should yield an average of ________________ with SD ________________.

(b)
Instead of a $20 discount, suppose that WMU students get a 5% discount on the monthly rent for all 1-bedroom apartments. The discounted monthly rent for the sample of 1-bedroom apartments should yield an average of ________________ with SD ________________.

(c)
If you took the 1-bedroom and 2-bedroom samples together, would the SD of their monthly rents be equal to $100, smaller than $100, or larger than $100?

7.
Golden delicious apples were packed in plastic bags for delivery. The filled bags averaged 9.5 pounds in weight, and the SD was .8 pounds.

(a)
The bags of apples are sold to a grocery chain, at a price of 30 cents per pound. (The heavier bags will, of course, cost more than the lighter bags.) The price per bag should average __________ dollars with SD __________ dollars.
(Hint: Price = (Weight)($.30).)

(b)
Suppose that the grocery chain uses their own trucks to pick up the bagged apples from the grower. For the trucking fee, they charge the grower 25 cents per bag. Therefore for each bag they pay a net price of (Weight)($.30)-$.25. The net price per bag should average __________ dollars with SD __________ dollars.


next up previous contents index
Next: Binomial and Normal Distributions Up: Location and Spread Previous: Calculating and S

2003-09-08