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
shusha [124]
3 years ago
6

Given a population with a mean of muμequals=100100 and a variance of sigma squaredσ2equals=3636​, the central limit theorem appl

ies when the sample size is ngreater than or equals≥25. A random sample of size nequals=2525 is obtained. a. What are the mean and variance of the sampling distribution for the sample​ means? b. What is the probability that x overbarxgreater than>101101​? c. What is the probability that 9898less than
Mathematics
1 answer:
lakkis [162]3 years ago
5 0

Answer:

a) \bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)

\mu_{\bar X}=100 \sigma^2_{\bar X}=1

b) P(\bar X >101)=1-P(\bar X

c) P(\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 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".  

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: P(A)+P(A') =1

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

X \sim N(\mu=100,\sigma=6)  

And let \bar X represent the sample mean, by the central limit theorem, the distribution for the sample mean is given by:  

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

a. What are the mean and variance of the sampling distribution for the sample​ means?

\bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)

\mu_{\bar X}=100 \sigma^2_{\bar X}=1.2^2=1.44

b. What is the probability that x overbarxgreater than>101

First we can to find the z score for the value of 101. And in order to do this we need to apply the formula for the z score given by:  

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}  

If we apply this formula to our probability we got this:  

z=\frac{101-100}{\frac{6}{\sqrt{25}}}=0.833  

And we want to find this probability:

P(\bar X >101)=1-P(\bar X

On this last step we use the complement rule.  

c. What is the probability that x bar 98less than

First we can to find the z score for the value of 98.

z=\frac{98-100}{\frac{6}{\sqrt{25}}}=-1.67  

And we want to find this probability:

P(\bar X

You might be interested in
What is the estimate 20 9/11 divided by 6 19/20?<br> A) 147<br> B) 120<br> C) 4<br> D) 3
ahrayia [7]

Answer:

D. 3

hope this helps

have a good day :)

Step-by-step explanation:

4 0
2 years ago
Two cars start driving in the same direction from the same place. If one travels 5050 mph and the other 5959 ​mph, how long will
vlabodo [156]

There is a 909 mph gap between the two cars. So if we can divide 3636 by 909 we get 4.


Answer: 4 Hours

8 0
3 years ago
Let f(x)=3(12)x+1. Which is equal to f(1)?
aalyn [17]

Answer:

just substitute the value of x as 1

f(x)=3(12)x+1

f(1)=3(12)(1)+1

f(1)=3(12)(1)+1

f(1)=36+1

f(1)=37

5 0
3 years ago
Rationalize the denominator of sqrt -9 / (4-7i) - (6-6i) ...?
Colt1911 [192]
√(- 9 ) / (( 4 - 7 i ) - ( 6 - 6 i )) = 3 i / ( 4 - 7 i - 6 + 6 i ) =
= 3 i / ( - 2 - i ) = - 3 i / ( 2 + i ) =
= \frac{-3i}{2 + i}* \frac{2 - i}{2 - i}= \\ =   \frac{-6i+3i ^{2} }{2- i^{2} }= \\ = \frac{-3-6i}{2+1}= \frac{-3-6i}{3}=
= - 1 - 2 i

5 0
3 years ago
Find the solutions to sin2(x) + cos(x) = 1, keeping 0 ≤ x &lt; 2π
frozen [14]
Sin2(x) +cos(x)=1
from the relation: (sin2(x) +cos2(x) =1 )
so , sin2(x)=1-cos2(x)
by subs. in the main eqn.
1-cos2(x) + cos(x) =1
by simplify the eqn.
cos(x) -cos2(x)=0
take cos(x) as a common factor
cos(x)* (1-cos(x))=0
then cos(x)=0 && cos(x)=1
cos(x)=0 if x= pi/2
& cos(x) = 1 if x = 0 , 2*pi
so the solution is x= {0,pi/2 , 2*pi}
3 0
3 years ago
Other questions:
  • a side of an equilateral triangle is 2/8 cm long. draw a picture that shows the triangle. what is the perimeter of the triangle?
    9·1 answer
  • If the sun of a number is tripled, the result is nine less than twice the number. Find the number
    10·1 answer
  • What is a balanced equation using numbers 9,7,2,1,6?
    5·1 answer
  • The school's production of Romeo and Juliet began at 7:30 P.M. The first act lasted 1 hour and 45 minutes. The act was followed
    14·2 answers
  • Solve the inequality-24≤×-3-8×​
    12·1 answer
  • Evaluate the operations on the given functions, f(x) and g(x), in the provided table
    15·1 answer
  • jose has 15 pencils tim has 5 times as many pencils as jose. jose wants to find out how many pencils tim has. he solves the prob
    7·1 answer
  • a firm wants to select a group of 8 out of its 20 employees to attend a Business trip .in how many ways can this be done if ther
    11·1 answer
  • Which expression can be used to check the answer to 56➗(-4)=-4?
    13·1 answer
  • 40% of the plants in Marcy's garden are root vegetables. If 20 plants are root vegetables, how many plants are in Marcy's garden
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!