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
mr Goodwill [35]
3 years ago
5

Consider a parent population with mean 75 and a standard deviation 7. The population doesn’t appear to have extreme skewness or

outliers.
a What are the mean and standard deviation of the distribution of sample means for n = 40?
b What’s the shape of the distribution? Explain your answer in terms of the Central Limit Theorem.
c What proportion of the sample means of size 40 would you expect to be 77 or less? If you use your calculator, show what you entered.
d Draw a sketch of the probability you found in part C.

Mathematics
1 answer:
Aleks04 [339]3 years ago
8 0

Answer:

a) \bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)

b) Since the sample size is large enough n>30 and the original distribution for the random variable X  doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

c) P(\bar X \leq 77)=P(Z

d) See figure attached

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable of interest. We know from the problem that the distribution for the random variable X is given by:

E(X) = 75

sd(X) = 7

We take a sample of n=40 . That represent the sample size

Part a

From the central limit theorem we know that the distribution for the sample mean \bar X is also normal and is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)

Part b

Since the sample size is large enough n>30 and the original distribution for the random variable X  doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

Part c

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}

And we want to find this probability:

P(\bar X \leq 77)=P(Z

We can us the following excel code: "=NORM.DIST(1.807,0,1,TRUE)"

Part d

See the figure attached.

You might be interested in
At a baseball game, 6 hotdogs cost $27. What is the cost of 1 hotdog? How many hotdogs can you buy for $18
Sergio [31]

Answer:

What is the cost of 1 hotdog?

Answer: $4.50

How many hotdogs can you buy for $18?

Answer: 4

Step-by-step explanation:

If $27 can buy you 6 hot dogs, to find the cost of one, we just divide.

27 divided by 6 = 4.5 ($4.50)

So 1 hotdog costs $4.50

If 1 hotdog is $4.50, and we want to know how much we can buy for $18, then we divide again.

18 divided by 4.5 = 4

So for $18, we can buy 4 hotdogs

8 0
2 years ago
Which system of equations has exactly one solution?
Hunter-Best [27]
If you put them in desmos online it works
4 0
3 years ago
Read 2 more answers
Job A offers an annual salary of $30,000 plus a bonus of 1% on sales. Job B offers an annual salary of $24,000 plus a bonus of 2
Tatiana [17]
Answer the equation is C to my calculations
7 0
3 years ago
Help me please <br><img src="https://tex.z-dn.net/?f=c-%2020%20%3D%204%20-%203c" id="TexFormula1" title="c- 20 = 4 - 3c" alt="c-
yKpoI14uk [10]

Answer:

c=6

Step-by-step explanation:

c-20-4-3c

c-20+20= 4+20-3c

c=24-3c

c+3c=24-3c + 3c

4c = 24

4c 4 24 4 =

c = 6

3 0
2 years ago
Read 2 more answers
What is the axis of symmetry of h(x) = 6x2 − 60x + 147?
Shalnov [3]
Hello : 
<span>h(x) = 6x² − 60x + 147= (x² -2(30)x+30²)-30²+147
</span>h(x) = (x-30)²-753 .....(vertex form)
<span>the axis of symmetry is the line of equation : x=30</span>
4 0
3 years ago
Read 2 more answers
Other questions:
  • If y= 1/4x and x = -12, find y.
    8·2 answers
  • 4,567.89
    8·1 answer
  • Angela uses 2/3 cup of strawberries to make 5/6 liter of smoothie what is the unit rate in cups of strawberries per liter of smo
    13·1 answer
  • What is 3/2m-m=4+1/2m
    6·1 answer
  • Radius=21 what is the cicumference​
    15·2 answers
  • A) 6 square meters<br> B) 16 square meters <br> C) 28 square meters <br> D) 49 square meters
    6·1 answer
  • Amelia has
    11·1 answer
  • Pls need this asap will give brainliest need it right now!!
    7·1 answer
  • Who is the father of modern Biology?<br>​
    6·2 answers
  • Pls help due in 10 minutes!!!
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!