Answer:
The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the population, we have that:
Mean = 0.5
Standard deviaiton = 0.289
Sample of 12
By the Central Limit Theorem
Mean = 0.5
Standard deviation 
The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.
Answer:
−22.599a−32.513
Step-by-step explanation:
Distribute:
= (4.1) (−7.93) + (4.1) (− 4.39 a) + − 4.6 a
= − 32.513 + − 17.999 a + − 4.6 a
Combine Like Terms:
= −32.513 + − 17.999 a + − 4.6 a
= (− 17.999 a + −4.6 a) + (− 32.513)
= − 22.599 a + (− 32.513) = − 22.599 a − 32.513
Answer:
Step-by-step explanation:
Let the consecutive even numbers be x,x+2,x+4, x+ 6, x+ 8 and x+10
So, the given condition is:
x+x+2+x+4+x+6+x+8+x+10 = 270
6x + 30 = 270
Subtracting both sides by 30
6x = 270 - 30
6x = 240
Dividing both sides by 6
x = 40
So,
First Number = x = 40
Second Number = x+2 = 40+2 = 42
Third Number = x+4 = 40+4 = 44
Fourth Number = x+6 = 40+6 = 46
Fifth Number = x+8 = 40+8 = 48
Sixth Number = x+10 = 40+10 = 50
Answer:
The margin of error for a 99% confidence interval for the population mean is 1.8025.
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
In this problem:
So
The margin of error for a 99% confidence interval for the population mean is 1.8025.
