The average hotel price in Moscow is $216 per night with a standard deviation of $32. The average hotel price in Cancun is $161 per night with a standard deviation of $22. The average hotel price in Bangkok is $100 per night with a standard deviation of $17. A room at the Emerald Hotel in Moscow costs $200 per night, a room at the Ocean View Hotel in Cancun costs $183 per night, and a room at the Emperor Hotel in Bangkok costs $120 per night.

Required:
Which hotel is more expensive compared to other hotels in its city?

Answer:

The Emperor Hotel in Bangkok has the higher z-score, so it is more expensive compared to other hotels in its city.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

The most expensive hotel has the higher z-score. So

Emerald Hotel in Moscow:

Costs $200, which means that [tex]X = 200[/tex]

The average hotel price in Moscow is $216 per night with a standard deviation of $32, which means that [tex]\mu = 216, \sigma = 32[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{200 - 216}{32}[/tex]

[tex]Z = -0.5[/tex]

Ocean View Hotel in Cancun

Costs $183, which means that [tex]X = 183[/tex].

The average hotel price in Cancun is $161 per night with a standard deviation of $22, which means that [tex]\mu = 161, \sigma = 22[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{183 - 161}{22}[/tex]

[tex]Z = 1[/tex]

Emperor Hotel in Bangkok

Costs $120, which means that [tex]X = 120[/tex].

The average hotel price in Bangkok is $100 per night with a standard deviation of $17, which means that [tex]\mu = 100, \sigma = 17[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{120 - 100}{17}[/tex]

[tex]Z = 1.18[/tex]

The Emperor Hotel in Bangkok has the higher z-score, so it is more expensive compared to other hotels in its city.

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