A consumer agency conducted a survey about the rates of double-bed rooms in hote

Question

A consumer agency conducted a survey about the rates of double-bed rooms in hotels.A survey of 100 hotels yielded a sample mean of $125, and a standard deviation of $24.

(a) (i) Calculate the z-scores for the room rates: $103, $139, $84 and $206.

(ii) Based on these z-scores,should any of these rates be classified as an outlier?

(b) If the z-score of a room rate exceeds 4, the consumer agency will label this rate as "outrageous". How much does a hotel need to charge for a room to be labeled outrageous"?

Explanation / Answer

X: Rates of double-bed rooms in hotels

Sample Mean rate of double-bed room = $125

Sample standard deviation = $24

(a)Z-score = (X-mean)/standard deviation

(i)

Z-Score for $103 = (103-125)/24 = -22/24 = -0.9167

Z-score for $139 = (139-125)/24 = 14/24 = 0.5833

Z-Score for $84 = (84-125)/24 = -41/24 = -1.7083

Z-score for $206 =(206-125)/24 = 81/24 = 3.375

(ii). Z-score > 3 or Z-score < -3 , are considered outliers.

As Z-score for $206 is 3.375 > 3 , $206 is considered as outlier

(b) Let X: be the rate as "outrageous". Then

Z-score for X > 4

(X-mean)/Standard deviation > 4

(X-125)/24 > 4

X-125 > 4 x 24 ; X-125 > 96 ; X > 125+96 ; X>221

Labeled outrageous: Hotel charge a room beyond $221

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.