t: Homework 1 Chapter 6 Assignment Score: 12.00% ructor Save Exit Submit Assignm

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t: Homework 1 Chapter 6 Assignment Score: 12.00% ructor Save Exit Submit Assignment for Grading Ouestion S of s Exercise 06.25 Algorithmic Check My Work (a remaining) New York City is the most expensive city in the United States for lodging. The mean hotel room rate is s205 per normally distributed with a standard deviation of sS6. Use Table 1 in Appendix B ). Assume that room rates are a. What is the probablity that a hotel room costs s227 or more per night (to 4 decimals? less than $143 per night (to 4 decimals)? c. what is the probablity that a hotel room costs between S200 and S299 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. Check My Work (a remaining) s Question 5 of 5 Exercise 06.25 Algorithmic Submit Assignment for Grading Cengage Learning I Cengage Technical Support

Explanation / Answer

Mean = 205

S.D. = 56

a)

P( X > 227)

Z score at X = 227

Z = (X - ) /
Z = (227 - 205) / 56

Z = 0.39286

From Z score table

P( X > 227) = P(Z > 0.393) = 0.3472

b)

P( X < 143)

Z score at X = 143

Z = (X - ) /
Z = (143 - 205) / 56
Z = -1.10714

From Z score table

P( X < 143) = P(Z < -1.107) = 0.1341

c)

P( 200 < X < 299)

Z score at X = 200

Z = (X - ) /
Z = (200 - 205) / 56
Z = -0.08929

Z score at X = 299

Z = (X - ) /
Z = (299 - 205) / 56
Z = 1.67857

From Z score table

P( 200<X < 299) = P(-0.089< Z < 1.679) = 0.489

d)

At P value at 20%

From Z score table Z value at P = 0 .20

Z = 0.84162

X value at Z = 0.84162

Z = (X - ) /
0.84162 = (X - 205) / 56
X = 205 + 47.131

X = 252.131

252.131 or more

P( X > 252.131) = 0.20

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