Question

In New York City the average hotel room costs $234 per night, with a standard deviation of $65. Suppose that you walk into a random hotel and learn their rate is $155 per night. If the rates are normally distributed, what is the probability that if you leave and walk into another random hotel, they will have a lower rate?

Answer 1

Since μ=234 and σ=65 we have:

P ( X<155 )=P ( X−μ<155−234 )=P ((X−μ)/σ<(155−234)/65)

Since (x−μ)/σ=Z and (155−234)/65=−1.22 we have:

P (X<155)=P (Z<−1.22)

Use the standard normal table to conclude that:

P (Z<−1.22)=0.1112

The required probability is 0.1112