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Case Problems Ch. 1
1.10 Architectural firms. Table 1.3 (page 13) gives the number of full-time staff employed by Indianapolis
architectural firms. Make a stemplot of the staff counts. What are the main features of the shape of this
distribution.
1.12 Yields of Treasury bills. Treasury bills are short-term borrowing by the U.S. government. They are
important in financial theory because the interest rate for Treasury bills is a “risk-free rate” that says what
return investors can get while taking (almost) no risk. More risky investments should in theory offer higher
returns in the long run. Here are the annual returns on Treasury bills from 1970 to 2004:
(a) Make a time plot of the returns paid by Treasury bills in these years.
(b) Interest rates, like many economic variables, show cycles, clear but irregular up-and-down movements. In
which years did the interest rate cycle reach temporary peaks?
(c) A time plot may show a consistent trend underneath cycles. When did interest rates reach their overall peak
during these years? Has there been a general trend downward since that year?
1.47 Privately held restaurant companies. The Forbes 500 list of the largest privately held companies
includes six restaurant-industry companies. Here they are, with
annual revenues in millions of dollars: A graph of only 6
observations gives little information, so we proceed to compute
the mean and standard deviation.
(a) Find the mean from its definition. That is, find the sum of the 6
observations and divide by 6.
(b) Find the standard deviation from its definition. That is, find the
deviations of each observation from the mean, square the
deviations, then obtain the variance and the standard deviation.
Example 1.13 shows the method.
(c) Now enter the data into your calculator and use the mean and standard deviation buttons to obtain and s. Do
the results agree with your hand calculations.
1.83 More on young men’s heights. The distribution of heights of young men is approximately Normal with
mean 69 inches and standard deviation 2.5 inches. Use the 68–95–99.7 rule to answer the following questions.
(a) What percent of these men are taller than 74 inches?
(b) Between what heights do the middle 95% of young men fall?
(c) What percent of young men are shorter than 66.5 inches?
1.86 Use Table A to find the proportion of observations from a standard Normal distribution that satisfies each
of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve
that is the answer to the question.