The high costs in the California real estate market have caused families who cannot afford to buy bigger homes to consider backyard sheds as an alternative form of housing expansion. Many are using the backyard structures for home offices, art studios, and hobby areas as well as for additional storage. The mean price of a customized wooden, shingled backyard structure is $3100 (Newsweek, September 29, 2003). Assume that the standard deviation is$1200.

What is the z-score for a backyard structure costing $2300?

The high costs in the California real estate market have caused families who cannot afford to buy bigger homes to consider backyard sheds as an alternative form of housing expansion. Many are using the backyard structures for home offices, art studios, and hobby areas as well
as for additional storage. The mean price of a customized wooden, shingled backyard structure is $3100 (Newsweek, September 29, 2003). Assume that the standard deviation is$1200.

The Newsweek article described a backyard shed-office combination built in Albany, California, for $13,000. Should this structure be considered an outlier? Explain.

Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 520, 650, 500, 450, and 280?

If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain.

The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours.

Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours.

The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes).

$$\begin{matrix} \text{Quarter-Mile Times:} & \text{0.92} & \text{0.98} & \text{1.04} & \text{0.9} & \text{0.99}\\ \text{Mile Times:} & \text{4.52} & \text{4.35} & \text{4.6} & \text{4.7} & \text{4.5}\\ \end{matrix}$$

After viewing this sample of running times, one of the coaches commented that the quartermilers turned in the more consistent times. Use the standard deviation and the coefficient of variation to summarize the variability in the data. Does the use of the coefficient of variation indicate that the coach’s statement should be qualified?

Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations.

Cooper Realty is a small real estate company located in Albany, New York, specializing primarily in residential listings. They recently became interested in determining the likelihood of one of their listings being sold within a certain number of days. An analysis of company sales of 800 homes in previous years produced the following data.

$$\begin{matrix} \text{ } & \text{ } & \text{Days } & \text{Listed} & \text{Until Sold}\\ \hline\\ \text{ } & \text{ } & \text{Under 30} & \text{31–90} & \text{Over 90} & \text{Total}\\ \text{ } & \text{Under \$150,000} & \text{50} & \text{40} & \text{10} & \text{100}\\ \text{Initial Asking Price} & \text{\$150,000–\$199,999} & \text{20} & \text{150} & \text{80} & \text{250}\\ \text{ } & \text{$200,000–$250,000} & \text{20} & \text{280} & \text{100} & \text{400}\\ \text{ } & \text{Over \$250000} & \text{10} & \text{30} & \text{10} & \text{50}\\ \hline\\ \text{ } & \text{Total} & \text{100} & \text{500} & \text{200} & \text{800}\\ \end{matrix}$$

If A is defined as the event that a home is listed for more than 90 days before being sold, estimate the probability of A.

Suppose that we have two events, $A$ and $B ,$ with $P ( A ) = .50 , P ( B ) = .60 ,$ and $P ( A \cap B ) = .40 .$

Find $P ( A | B )$ .

A data set with roughly a bell-shaped distribution has mean 45 and standard deviation 12. Approximately what percentage of the observations lie between 33 and 57?

The following payments and receipts are related to land, land improvements, and buildings acquired for use in a wholesale ceramic business. The receipts are identified by an asterisk.
a. Fee paid to attorney for title search. . . . . . . . . . . . . . . . . . . . . . . . . . . . $\hspace{3pt} \$\hspace{10pt} 1,500$
b. Cost of real estate acquired as a plant site: Land . . . . . . . . . . . . . . . . $\hspace{8pt} 270,000$
$\hspace{163pt}$ Building . . . . . . . . . . . . . $\hspace{12pt} 30,000$
c. Special assessment paid to city for extension of water main to the
property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $\hspace{9pt} 20,000$
d. Cost of razing and removing building . . . . . . . . . . . . . . . . . . . . . . . . . . $\hspace{14pt} 5,000$
e. Proceeds from sale of salvage materials from old building . . . . . . . . $\hspace{14pt} 3,600 \text{*}$
f. Delinquent real estate taxes on property, assumed by purchaser . . . $\hspace{8pt}15,800$
g. Premium on one-year insurance policy during construction . . . . . . . $\hspace{12pt} 4,200$
h. Cost of filling and grading land . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $\hspace{7pt} 17,500$
i. Architect’s and engineer’s fees for plans and supervision . . . . . . . . . . $\hspace{7pt} 18,000$
j. Money borrowed to pay building contractor. . . . . . . . . . . . . . . . . . . . . $\hspace{4pt} 750,000 \text{*}$
k. Cost of repairing windstorm damage during construction. . . . . . . . . $\hspace{12pt} 4,500$
l. Cost of paving parking lot to be used by customers . . . . . . . . . . . . . . $\hspace{8pt}15,000$
m. Cost of trees and shrubbery planted . . . . . . . . . . . . . . . . . . . . . . . . . . $\hspace{15pt} 9,000$
n. Cost of floodlights installed on parking lot . . . . . . . . . . . . . . . . . . . . . $\hspace{15pt} 1,100$
o. Cost of repairing vandalism damage during construction . . . . . . . . $\hspace{15pt} 1,500$
p. Proceeds from insurance company for windstorm and vandalism damage
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $\hspace{16pt} 6,000\text{*}$
q. Payment to building contractor for new building . . . . . . . . . . . . . . . $\hspace{5pt} 800,000$
r. Interest incurred on building loan during construction. . . . . . . . . . . $\hspace{9pt} 45,000$
s. Refund of premium on insurance policy (g) canceled after 11 months $\hspace{10pt} 350\text{*}$
$\textsf{\textcolor{#4257b2}{Instructions}}$
$1$. Assign each payment and receipt to Land (unlimited life), Land Improvements (limited life), Building, or Other Accounts. Indicate receipts by an asterisk. Identify each item by letter and list the amounts in columnar form, as follows:

$$\begin{array}{ccccc} && \textbf{Land} && \textbf{Other}\\ \textbf{Item} & \textbf{Land} & \textbf{Improvements} & \textbf{Building} & \textbf{Accounts}\\ \hline \end{array}$$

$2$. Determine the amount debited to Land, Land Improvements, and Building.
$3$. The costs assigned to the land, which is used as a plant site, will not be depreciated, while the costs assigned to land improvements will be depreciated. Explain this seemingly contradictory application of the concept of depreciation.

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y=1+ secx, y =3; about y=1

Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges:

20 to 40

The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline was $2.05 (Energy Information Administration, May 2009). Suppose that the standard deviation was$.10 and that the retail price per gallon has a bellshaped distribution. a. What percentage of regular grade gasoline sold between $1.95 and$2.15 per gallon? b. What percentage of regular grade gasoline sold between $1.95 and$2.25 per gallon? c. What percentage of regular grade gasoline sold for more than $2.25 per gallon?