New York City is the most expensive city in the United States for lodging. The m

Question

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $56. Use Table 1 in Appendix B. a. What is the probability that a hotel room costs $226 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 $200 and $301 per nigh (to 4 decimals)? d. or Select your answer

Explanation / Answer

mean = 205 , s = 56

a)
P(x > 226)

z = ( x - mean) / s
= ( 226 -205) / 56
= 0.375

we need to find P(z > 0.375)

P(x > 226 ) = P(z >0.375) = 0.3538

b)
P(x <141)

z = ( x - mean) / s
= ( 141 - 205) / 56
= -1.143

we need to find P(z <-1.143)

P(x <141) = P(z <-1.143) = 0.1265

c)
P(200 < x < 301)

z = (P( 200 - 205) /56) < z < P((301 - 205) / 56)
= P(-0.089 < z < 1.714)

we need to find P(-0.089 < z < 1.714)

P(200 < x < 301) = P(-0.089 < z < 1.714) = 0.4923

c)
z value for the top 20% = 0.842

z = (x - mean) / s
0.842 = ( x - 205) /56
x = 252.152

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