Question

suppose the nightly rate for a three star hotel in paris is thought to be bell-shaped and symmetrical with a mean of 160 euros and a standard deviation of 8 euros. The percentage of hotels with rates between 144 and 176 eruos is_________

Answer 1

Answer:

95.44%

Step-by-step explanation:

Mean rate (μ) = 160 euros

Standard deviation (σ) = 8 euros

For any given rate, X, the z-score is:

$z=\frac{X-\mu}{\sigma}$

For X = 144 euros:

$z=\frac{144-160}{8}\\ z=-2$

For X= 176 euros

$z=\frac{176-160}{8}\\ z=2$

In a standard distribution, a z-score of -2 corresponds to the 2.28th percentile, while a z-score of 2 corresponds to the 97.72th percentile.

Therefore, the percentage of hotels with rates between 144 and 176 euros is:

$P=97.72-2.28\\P=95.44\%$