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
Wewaii [24]
3 years ago
7

A sample of size 6 will be drawn from a normal population with mean 61 and standard deviation 14. Use the TI-84 Plus calculator.

Is it appropriate to use the normal distribution to find probabilities for x?
Mathematics
1 answer:
AVprozaik [17]3 years ago
8 0

Answer:

X \sim N(61,14)  

Where \mu=61 and \sigma=14

Since the distribution for X is normal then the distribution for the sample mean  is also normal and given by:

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

\mu_{\bar X} = 61

\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715

So then is appropiate use the normal distribution to find the probabilities for \bar X

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  The letter \phi(b) is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: \phi(b)=P(z

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(61,14)  

Where \mu=61 and \sigma=14

Since the distribution for X is normal then the distribution for the sample mean \bar X is also normal and given by:

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

\mu_{\bar X} = 61

\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715

So then is appropiate use the normal distribution to find the probabilities for \bar X

You might be interested in
Which is the simplified form of (9c^-9)^-3<br> b 1/729 c^27
rosijanka [135]

<u>ANSWER</u>

(9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729}

<u>EXPLANATION</u>

The given expression is

(9 {c}^{ - 9} )^{ - 3}

Recall that:

({a}^{m} )^{n}  =  {a}^{mn}

We use the law of exponents to get

(9 {c}^{ - 9} )^{ - 3}  = 9^{ - 3}  {c}^{ - 9 \times  - 3}

Let us multiply in the exponents to get:

(9 {c}^{ - 9} )^{ - 3}  = 9^{ - 3}  {c}^{ 27}

Recall again that:

{a}^{ - m}  =  \frac{1}{ {a}^{m} }

This implies that:

(9 {c}^{ - 9} )^{ - 3}  =  \frac{1}{ {9}^{ 3} }  \times {c}^{ 27}

We expand the power to get:

(9 {c}^{ - 9} )^{ - 3}  =  \frac{1}{9 \times 9 \times 9} \times {c}^{ 27}

(9 {c}^{ - 9} )^{ - 3}=\frac{1}{729}  \times {c}^{ 27}

We multiply out to get:

(9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729}

7 0
2 years ago
You roll two six-sided fair nukber cubes.Whatbis the probability that you will roll snake eyes(both ones)?
Katyanochek1 [597]

Answer:

1/36

Step-by-step explanation:

Each dice has a 1 in 6 chance to land on a 1, but for both dice to land on 1's it would be (\frac{1}{6} )(\frac{1}{6})=\frac{1}{36}

3 0
2 years ago
PLEASE HELP ITS DUE SOON!!!!
Anvisha [2.4K]
Heberto could go 14 blocks East and 14 blocks south, so the last answer
3 0
2 years ago
The scale of a map is 1 : 25 000
Artyom0805 [142]

Answer: 5.5km

Step-by-step explanation:

The scale given 1 : 25 000 , and it was said that on the map , the distance between two railway stations is 22 cm , this means that the scale of the map is 1: 25000 cm.

The scale 1 : 25 000 means that each centimeters on the map represent 25 ,000 in real life ,therefore , to calculate the real distance between the two railway station , we have

25,000 X 22

= 550000 cm

To convert this to km

Recall that

1 km = 100,000 cm

Therefore we will divide the answer by 100,000 , that is

550000/100000

= 5.5 km

Therefore , the real distance between the two railway stations is 5.5km

7 0
3 years ago
Math problem help plz <br> (don't send links will report u)<br> ASAp
ozzi
I think the answer is c- reflection
5 0
2 years ago
Other questions:
  • A farmer wants to make a rectangular grazing area for his cows. He will use one side of his barn and fence the other three sides
    10·1 answer
  • The sum of three consecutive integers is 9. What is the equation that represents the scenario?
    13·2 answers
  • Y=(x-4)(x+20) find vertex
    12·1 answer
  • Justin wants to use 376ft of fencing to fence off the greatest possible rectangular area for a garden. What dimensions should he
    5·1 answer
  • If f(x)=3x^2-1 and g(x)=x+2, find (f+g)(x)
    13·2 answers
  • On eight book shelves there are 44 books per shelf. How many books are there altogether? If 1/4 of these books are novels, how m
    6·1 answer
  • А
    9·1 answer
  • 15 + ( -11)3 please help
    6·2 answers
  • Find the length of the unknown segment (x) in each figure. Use theorem of secant segment and
    7·1 answer
  • You need red and blue ribbon for a craft project. The instructions say that the red ribbon should be 7 inches longer than the bl
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!