Question

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night.† Assume that room rates are normally distributed with a standard deviation of $55.

(a)

What is the probability that a hotel room costs $245 or more per night? (Round your answer to four decimal places.)

(b)

What is the probability that a hotel room costs less than $120 per night? (Round your answer to four decimal places.)

(c)

What is the probability that a hotel room costs between $210 and $300 per night? (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 204

standard deviation = = 55

a) P(x 245 ) = 1 - P(x   245 )

= 1 - P[(x - ) / (245-204) /55 ]

= 1 -  P(z 0.75)  

= 1 - 0.7422 = 0.2578

probability = 0.2578

b)

P(x <120 ) = P[(x - ) / < ( 120-204) / 55]

= P(z < -1.53 )

= 0.0516

probability = 0.0516

c)

P( 210< x < 300 ) = P[(210- 204)/ 55) < (x - ) /  < (300-204) /55 ) ]

= P( 0.11< z < 1.75)

= P(z <1.75 ) - P(z < 0.11)

= 0.9505 - 0.504 = 0.4465

Probability = 0.4465

  

Probability =