Question

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.

Answer 1

42 4= 3100 , = 1200 ,2=* ~N(0,1) 2300-3100 1200 22312.03100 = 1-0.67 2- 4900 – 3100 = |1.50 ] © 49 0-3100 1.50 1200 @ is below 0.67 Standard dev. from mean. while ③ is above 1.50 Standard dev. from meam. Two outlier because value is within 2 sidev. © 13000-3100 2 2- 13000 – 3100 18,25 = 1200 Yes, it is an outlier beccesse it is above 2 Slemdard der, from the meam. CS Scanned with C CamScanner