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Answer:
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 30 and standard deviation 0.1.
Step-by-step explanation:
Central Limit Theorem
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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
The batteries produced in a manufacturing plant have a mean time to failure of 30 months with a standard deviation of 2 months.
This means that
Sample of 400 batteries. The sampling distribution of is approximately:
So
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 30 and standard deviation 0.1.
So what we know is that 15 is the diameter
However the formula to find the area of a circle is A=
r²
So to convert the 15 in diameter to a radius you have to do 15÷2,which is equal to 7.5
Now we know that the radius is 7.5.
So what we do now is A=7.5²
Then after we find what 7.5² is we get A=56.25
Then what we do is 3.14×56.25, because pi= 3.14.
So when we do 3.14×56.25, we get 176.625
So the answer is A= 176.6 in²
However the formula to find the area of a circle is A=
So to convert the 15 in diameter to a radius you have to do 15÷2,which is equal to 7.5
Now we know that the radius is 7.5.
So what we do now is A=
Then after we find what 7.5² is we get A=
Then what we do is 3.14×56.25, because pi= 3.14.
So when we do 3.14×56.25, we get 176.625
So the answer is A= 176.6 in²