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
Morgarella [4.7K]
3 years ago
9

According to the local real estate board, the average number of days that homes stay on the market before selling is 78.4 with a

standard deviation equal to 11 days. A prospective seller selected a random sample of 36 homes from the multiple listing service. Above what value for the sample mean should 95 percent of all possible sample means fall?
Mathematics
1 answer:
Colt1911 [192]3 years ago
7 0

Answer:

95 percent of all possible sample means fall above 75.30 days.

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 = 78.4, \sigma = 11, n = 36, s = \frac{11}{\sqrt{36}} = 1.8333

Above what value for the sample mean should 95 percent of all possible sample means fall?

Above the 100-95 = 5th percentile.

5th percentile:

X when Z has a pvalue of 0.05. So X when Z = -1.645.

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

By the Central Limit Theorem

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

-1.645 = \frac{X - 78.4}{1.8333}

X - 78.4 = -1.645*1.8333

X = 75.30

95 percent of all possible sample means fall above 75.30 days.

You might be interested in
100 POINTS AND BRAINIEST TO BEST CORRECT ANSWER!
tresset_1 [31]

Answer:

The answer is B causation only.

Step-by-step explanation:

The answer is causation only because as the miles walked increases the number of calories burned also increases. Causation also exist because the miles walked is causing the calories to be burned.

8 0
3 years ago
Read 2 more answers
How many miles equal 26 kilometers? [1 kilometer = 0.62 mile]
Sati [7]
1 km = 0.62 miles....so 26 km = (26 * 0.62) = 16.12 miles
5 0
3 years ago
Read 2 more answers
A chef uses 2 3 cup of flour for every 1 8 cup of water in a dough recipe. If the chef follows the recipe proportions, which sta
VashaNatasha [74]

Step-by-step explanation:

A chef uses 2/3 cup of flour for every 1/8 cup of water in a dough recipe.

It means,

2/3 cup = 1/8 cup of water

1\ \text{cup}=\dfrac{\dfrac{1}{8}}{\dfrac{2}{3}}\\\\=0.1875

Hence, the constant of proportionality is 0.1875.

5 0
2 years ago
90 - 15 x 12 divided 6 Plz help! I’ll give some points!
PilotLPTM [1.2K]
I believe it’s 900. Yeah, I think the answer is 900.
3 0
3 years ago
Read 2 more answers
Please help me solve this whole problem!
Dvinal [7]
I’m not good at math srry but hope someone answers the is for you
3 0
2 years ago
Read 2 more answers
Other questions:
  • A ramp is 17 ft long , rises 8 ft above the floor, and covers a horizontal distance of 15 ft,as shown in the figure
    5·1 answer
  • 8. Teo makes a necklace of x wooden beads at $0.50
    9·1 answer
  • A bacteria culture begins with eight bacteria which triple in size every week. how many bacteria exist in the culture after four
    7·1 answer
  • I don’t know how to do this can someone help me please i put 30 points...
    10·1 answer
  • How to complete the equation of the line through (2,-2) and (4,1)
    15·1 answer
  • Solve for x<br> 5х – 12 = 3х + 10
    7·1 answer
  • Help this is due tomorrow​
    10·1 answer
  • If Cara works 14 hours, she earns $84. If she works 19 hours, she earns $114. Let y represent the total amount of money that Car
    11·1 answer
  • A delivery truck has 40,000 miles on its odometer and travels an average of 22,000 miles per year.
    10·1 answer
  • This Stem-and-Leaf Plot shows the number of people who attended a local nine-day carnival.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!