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Answer:
0.9 can be written as a fraction
Step-by-step explanation:
0.9 written as a fraction
if we have no denominator at the bottom then we put 1 at the bottom
0.9 can be written as
Now we need to remove the decimal point
we have 9 after the decimal point. one number after the decimal point.
To remove the decimal point we multiply both top and bottom by 10
0.9 can be written as a fraction
Answer:
The point estimate is 5,617.
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
The 98% confidence interval for the difference between the two population means is (5163, 6071).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Compound 1:
127 brakes, average brake life of 42,814 miles, population standard deviation of 1819 miles. This means that:
Compound 2:
163 brakes, average brake life of 37,197 miles, population standard deviation of 1401 miles. This means that:
Distribution of the difference:
The point estimate is 5,617.
Confidence interval
The confidence interval is:
In which
z is the z-score that has a p-value of .
The margin of error is:
98% confidence level
So , z is the value of Z that has a p-value of
, so
.
Margin of error:
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
For the confidence interval, as we round to the nearest whole number, we round it 454. So
The lower bound of the interval is:
The upper bound of the interval is:
The 98% confidence interval for the difference between the two population means is (5163, 6071).
The option first “shift right 1 unit, reflect over the y-axis, and then vertically stretch by a factor of 3” is correct.
<h3>What is linear equation?</h3>It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a function f(x) = x
The above function represents a linear function.
As we can see in the graph of a function g(x)
f(x) = x
First shift right 1 unit
f(x) = x -1
Then reflect over y-axis
f(x) = -x - 1
Then stretch by a factor of 3
f(x) = -3x - 1
Thus, the option first “shift right 1 unit, reflect over the y-axis, and then vertically stretch by a factor of 3” is correct.
Learn more about the linear equation here:
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