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?

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 ...