Many families in California are using backyard structures fo

Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is $3100. Assume that the standard deviation is $1200.

a. What is the z-score for a backyard structure costing $2300?
b. What is the z-score for a backyard structure costing $4900?
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain.

Solution

(a)Z=(X-mean)/s = (2300-3100)/1200

=-0.67

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(b)Z=(X-mean)/s = (4900-3100)/1200

=1.5

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(c) part (b) should be considered an outlier.

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(d) Yes, this structure be considered an outlier because the Z-score is very larger.