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
alexira [117]
3 years ago
5

The mean rent of a 3-bedroom apartment in Orlando is $1300. You randomly select 10 apartments around town. The rents are normall

y distributed with a standard deviation of $350. What is the probability that the mean rent is more than $1100?
Mathematics
1 answer:
lana [24]3 years ago
7 0

Answer:

96.49% probability that the mean rent is more than $1100

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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 1300, \sigma = 350, n = 10, s = \frac{350}{\sqrt{10}} = 110.68

What is the probability that the mean rent is more than $1100?

This is 1 subtracted by the pvalue of Z when X = 1100. So

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

By the Central Limit Theorem

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

Z = \frac{1100 - 1300}{110.68}

Z = -1.81

Z = -1.81 has a pvalue of 0.0351

1 - 0.0351 = 0.9649

96.49% probability that the mean rent is more than $1100

You might be interested in
Daniel reads dor 8 times as many as April. Daniel read 44 minutes this week. How many minutes does April read?
ELEN [110]
44 [minutes] * 8 [times as many as April] = 352 [minutes in April]
5 0
2 years ago
(2x-8)(2x+9) help please​
lesya [120]

(2x - 8)(2x + 9) \\ 4 {x}^{2}  + 18x - 16x - 72 \\ 4 {x}^{2}  + 2x - 72

HOPE IT HELPS

PLEASE GIVE BRAINLIEST

4 0
2 years ago
Read 2 more answers
Can you Complete the table please?
Lisa [10]

Answer:


Step-by-step explanation:

Bike 12.7 percent, decreases

Scooter 24 percent, increase

Tennis racket, 82.95

Skis 452.40

5 0
3 years ago
Solve simultaneously :<br>a) y=2x-3<br> 2y+x=4​
Dimas [21]

Answer:

hope this helps you

have a great day

4 0
2 years ago
Folgers coffee is priced at 12.88 for 80 cups of coffee, and Seattle's best is priced at 9.00 for 50 cups which brand of coffee
Akimi4 [234]

Answer:

At approximately

16 c a cup, Folgers Coffee is better value than Seattle's Best which costs

18 c a cup.

6 0
3 years ago
Other questions:
  • 5x + 45 = 1605 im too lazy to do this thx
    5·2 answers
  • Question 2 Multiple Choice Worth 4 points)
    8·1 answer
  • AABC ~ AQRS
    8·1 answer
  • Find the opposite of 4p3+9p−2 .
    12·1 answer
  • Yesterday, there were b milligrams of bacteria in a lab experiment. Today, there are b^2 milligrams of bacteria. If there are 40
    8·1 answer
  • Simplify (y+1)^5 ÷ (y+1)^2
    5·1 answer
  • The perimeter of a rectangular pool is 306m. If the length of the pool is 87m, what is its width?
    7·1 answer
  • Draw a number line -5through 5 and mark 0≤x≤2
    6·1 answer
  • Line d is parallel to line c in the figure below. Parallel lines d and c are intersected by lines q and p to form 2 triangles. A
    5·1 answer
  • Find the measure of the indicated angle
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!