Question

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $54. Use Table 1 in Appendix B.

a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)?

b. What is the probability that a hotel room costs less than $141 per night (to 4 decimals)?

c. What is the probability that a hotel room costs between $199 and $300 per night (to 4 decimals)?

d. What is the cost of the 20% most expensive hotel rooms in New York City? Round up to the next dollar.

Answer 1

Given that mean = 204 and standard deviation = 54

(A) we have to find P(X>225)

using normalcdf

setting lower = 225, upper = 999, mean = 204 and standard deviation = 54

we get

P(X>225) = normalcdf(225,999,204,54)

= 0.3487

(B)

we have to find P(X<141)

using normalcdf

setting lower = -999, upper = 141, mean = 204 and standard deviation = 54

we get

P(<141) = normalcdf(-999,141,204,54)

= 0.1217

(C)

we have to find P(199<X<300)

using normalcdf

setting lower = 199, upper = 300, mean = 204 and standard deviation = 54

we get

P(199<X<300) = normalcdf(199,300,204,54)

= 0.4992

(D) Using invNorm

setting area = 0.80 (because for top 20%, area under the curve is 1-0.2 = 0.80)

mean = 204

standard deviation = 54

we get

Required Cost X = invNorm(0.80,204,54)

= 250 (rounded to next dollar)