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 $135, and a standard deviation of $24 (a) Find the z-scores for the room rates: $89, $172, $215. Based on these z-scores, which of the rates can be considered 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"?

Answer 1

Z = (X - $\mu$) / s

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(a) For X = $89, Z = (89 - 135)/24 = -1.92

For X = $172, Z = (172 - 135)/24 = 1.54

For X = $215, Z = (215 - 135)/24 = 3.33

An outlier is any Z score > 3 or any Z score < -3

Therefore the rate of $215 can be considered as an outlier as its Z score is > 3.

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(b) To be labelled outrageous Z should be greater than 4

If Z is equal to 4, then the rate is calculated as

4 = (X - 135) / 24

Solving for X; X = (24 * 4) + 135 = 96 + 135 = $231

At $231, Z is = 4. Therefore to be labeled outrageous the hotel needs to charge $232

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