1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Soloha48 [4]
3 years ago
14

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 $55.
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 $140 per night (to 4 decimals)?
c. What is the probability that a hotel room costs between $200 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.
Mathematics
1 answer:
Simora [160]3 years ago
4 0

Answer:

a) 0.3520 = 35.20% probability that a hotel room costs $225 or more per night.

b) 0.1038 = 10.38% probability that a hotel room costs less than $140 per night.

c) 0.4878 = 48.78% probability that a hotel room costs between $200 and $300 per night.

d) $251.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 204, \sigma = 55

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

This probability is 1 subtracted by the pvalue of Z when X = 225. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{225 - 204}{55}

Z = 0.38

Z = 0.38 has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

0.3520 = 35.20% probability that a hotel room costs $225 or more per night.

b. What is the probability that a hotel room costs less than $140 per night (to 4 decimals)?

This probability is the pvalue of Z when X = 140. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{140 - 204}{55}

Z = -1.16

Z = -1.16 has a pvalue of 0.1038.

0.1038 = 10.38% probability that a hotel room costs less than $140 per night.

c. What is the probability that a hotel room costs between $200 and $300 per night (to 4 decimals)?

This probability is the pvalue of Z when X = 300 subtracted by the pvalue of Z when X = 200. So

X = 300

Z = \frac{X - \mu}{\sigma}

Z = \frac{300 - 204}{55}

Z = 1.75

Z = 1.75 has a pvalue of 0.9599.

X = 200

Z = \frac{X - \mu}{\sigma}

Z = \frac{200 - 204}{55}

Z = -0.07

Z = -0.07 has a pvalue of 0.4721.

0.9599 - 0.4721 = 0.4878

0.4878 = 48.78% probability that a hotel room costs between $200 and $300 per night.

d. What is the cost of the 20% most expensive hotel rooms in New York City?

This is X when Z has a pvalue of 1-0.2 = 0.8. So X when Z = 0.84

Z = \frac{X - \mu}{\sigma}

0.84 = \frac{X - 204}{55}

X - 204 = 0.84*55

X = 250.2

Rounding to the next dollar.

$251.

You might be interested in
A hot air balloon is 910 feet above sea level. It is rising at a rate of 4 feet fee second. How high is the hot air balloon afte
nalin [4]

Answer:

1230

Step-by-step explanation:

80 x 4 = 320

320 + 910 = 1230

5 0
1 year ago
write an expression in simplest form that represents the total amount in each situation: Today is your friends birthday. she is
Vilka [71]

Answer:

2y-5

Step-by-step explanation:

friend: y

Brother: y-5

y+y-5

aka

2y-5

7 0
3 years ago
Identify the transformation that carries the figure onto itself.
Alenkinab [10]

Rotation as you could rotate it 360 degrees back into its original place

8 0
3 years ago
Emily is going to invest in an ascount paying an interest rate of 4.4% compounded
sp2606 [1]
I’m not sure about this one I’m sorry I couldn’t help
3 0
3 years ago
The formula to find the surface area of a cube is 6s to the power of 2, where s stands for the side length of the cube. What is
gladu [14]
The surface area of the cube is 600cm^2.

6(10^2)
6(100)
600
3 0
3 years ago
Other questions:
  • Find the value of Log2 32=y
    10·1 answer
  • In the figure below, ∆ABC is similar to ∆DBE. Given that BE=10cm, AB=3cm and BD=4cm. Find the length of BC.
    8·1 answer
  • keith had 81/2 cups of flour. he used 52/3 cups to make bread. how many cups of flour does keith have left?
    9·1 answer
  • A rectangular folder has a perimeter of 30 inches and an area of 54 square inches. What are the dimensions of the folder?
    8·1 answer
  • Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260 person-hour
    14·1 answer
  • (b) Suppose you pay the loan off after 2 years. How much interest do you save by paying the loan off
    15·1 answer
  • In a survey of a town, 54% of residents own a car, 34% of residents own a truck, and 11% of residents own both a car and a truck
    7·1 answer
  • Solve the graph fjsdjshfdkjfd
    12·1 answer
  • Please help me with this math problem!! NO LINKS PLEASE!! :)
    9·1 answer
  • Consider the expression.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!