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
solniwko [45]
3 years ago
14

Suppose monthly rental prices for a one-bedroom apartment in a large city has a distribution that is skewed to the right with a

population mean of $880 and a standard deviation of $50.
(a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?
(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?
Mathematics
1 answer:
omeli [17]3 years ago
8 0

Answer:

a) Nothing, beause the distribution of the monthly rental prices are not normal.

b) 1.43% probability that the sample mean rent price will be greater than $900

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

(a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?

Nothing, beause the distribution of the monthly rental prices are not normal.

(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?

Now we can apply the Central Limit Theorem.

\mu = 880, \sigma = 50, n = 30, s = \frac{50}{\sqrt{30}} = 9.1287

This probability is 1 subtracted by the pvalue of Z when X = 900.

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

By the Central Limit Theorem

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

Z = \frac{900 - 880}{9.1287}

Z = 2.19

Z = 2.19 has a pvalue of 0.9857

1 - 0.9857 = 0.0143

1.43% probability that the sample mean rent price will be greater than $900

You might be interested in
PLEASE HELP ME I AM HORRIBLE AT TRIGONOMETRY!!! TRIANGLES ARE SO HARD!!!
OleMash [197]

Answer:

A construction worker may use trigonometry when building the roof of a house. They may have to calculate the right angle that hypotenuse must sit at so water doesn't build up on the roof and cause leaks.

(this may be more of an architect's job, as they are the ones that design the houses)

or

An air traffic controller may use trigonometry to find how long it will take an airplane to land/how far the airplane is from the ground while it is in the sky (hypotenuse), based on its height from the ground (opposite) and the distance away from the runway it is (adjacent). They can also calculate the angle of elevation of the airplane from the tower they work in.

8 0
2 years ago
IF THIS QUESTION IS EASY MAKE ME BRILLIST WHAT IS 10 X 6 ?
Dmitriy789 [7]

Answer:

its 60

Step-by-step explanation:

please mark brainliest

6 0
3 years ago
Read 2 more answers
The Kuroshio Sea tank is 27m long, 35m wide and 10m deep. What is the volume of the tank? Show your
umka21 [38]

The volume of Kuroshio Sea rank is 9450 cubic meters, if the sea tank is  27m long, 35m wide and 10m deep.

Step-by-step explanation:

The given is,

                 Kuroshio Sea tank is 27m long, 35m wide and 10m deep.

Step:1

                Sea tank looks like a rectangular prism,

                 Formula to calculate the volume of rectangular prism,

                                   Volume, V =whl.............................(1)

                Where, w - Width of the rectangular prism

                              h - Height or depth of the rectangular prism

                               l - Length of the rectangular prism

              From given,

                       w = 35 meters

                         l = 27 meters

                        h = 10 meters

             Equation (1) becomes,

                                              V = (35)(10)(27)

                                                  = (945)(10)

                                                 =9450

      Volume of the sea tank, V = 9450 Cubic meters

Result:

         The volume of Kuroshio Sea rank is 9450 cubic meters, if the sea tank is  27m long, 35m wide and 10m deep.

           

3 0
3 years ago
-3x &gt; 15 or 2x -1 &gt; 7<br> NEED HELP ASAP !!!
Artyom0805 [142]

Answer:

no.

Step-by-step explanation:

never.

5 0
3 years ago
8) The total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh?​
nirvana33 [79]

Answer:

120 pounds I think

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • F(t)=3t^2-2 , find f(k-2)
    15·1 answer
  • A group of random people were polled about whether they prefer to communicate using text messages or by phone calls. The results
    5·2 answers
  • Write an equation in​ point-slope form of the line that passes through the given​ points, then write the equation in​ slope-inte
    5·1 answer
  • What is 7 10ths minus 4 10ths
    7·2 answers
  • The graph represents function 1 and the equation represents function 2:
    6·1 answer
  • PLEASE HELP!!! <br> Shade 30% of the whole grid.<br> How much blocks do i shade?
    12·1 answer
  • FOR 43 POINTS PLEASE HELP I don't want to fail I need as much help as i can get
    14·2 answers
  • Given the sequence 7, 12, 17, 22
    9·2 answers
  • Elizabeth is organizing dessert plates with 15 brownies and 9 chocolate chip cookies. If she wants all the plates to be exactly
    10·1 answer
  • PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*.. <br> IM GIVING 40 POINTS !! DONT SKIP :((.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!