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. What is the percentage of hotels with rates between 144 and 176​ euros?

Answer 1

Using the Empirical Rule for a bell-shaped distribution, we find that approximately 95% of the hotel rates are between 144 and 176 euros.

Step-by-step explanation:

The question asks for the percentage of hotels with rates between 144 and 176 euros given a bell-shaped and symmetrical distribution of nightly rates for a three-star hotel in Paris, with a mean of 160 euros and a standard deviation of 8 euros. To solve this, we can apply the Empirical Rule which states that approximately 95% of data within a bell-shaped distribution lies within two standard deviations of the mean.

Calculating two standard deviations from the mean (160 ± (2 × 8)), we get the range from 144 to 176 euros. Therefore, using the Empirical Rule, we can conclude that approximately 95% of the hotel rates fall within the given range.

Answer 2

95.44% of hotels are with rate between 144 and 176 euros

Step-by-step explanation:

Given

Mean = μ = 160 euros

SD = σ = 8 euros

We have to find the z-scores for both values

So,

z-score for 144 = z_1 = (x-μ)/σ = (144-160)/8 = -16/8 = -2

z-score for 176 = z_2 = (x-μ)/σ = (176-160)/8 = 16/8 = 2

Now the area to the left of z_1 = 0.0228

Area to the left of z_2 = 0.9772

Area between z_1 and z_2 = z_2-z_1

= 0.9772-0.0228

=0.9544

Converting into percentage

95.44%

Therefore, 95.44% of hotels are with rate between 144 and 176 euros..