What is the product of 25 and (6/5n + 3 1/4)
1 answer:
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Answer:
a) -6 mpg.
b) 2.77 mpg
c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.
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
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.
Gas mileage A: Mean 36, standard deviation 6, sample of 50:
So
Gas mileage B: Mean 42, standard deviation 8, sample of 50:
So
Distribution of the difference:
Mean:
Standard error:
A. Find the point estimate.
This is the difference of means, that is, -6 mpg.
B. Find the margin of error
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 .
That is z with a pvalue of , so Z = 1.96.
Now, find the margin of error M as such
The margin of error is of 2.77 mpg
C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)
The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg
The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg
The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
Answer:
a)
S+G=525
G=S+75
b) See attached pictures
c) S=$225 and G=$300
The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.
Step-by-step explanation:
a) For the first part of the problem, the addition of both amounts will give us the total, so the first equation is:
S+G=525.
On the second equation we need to add 75 to sharon's amount to figure Geordi's amount, so we get:
G=S+75
b) In order to graph the system of equations, we need to find two points for each of the equations. It would be a good idea to solve the first equation for g, so our system of equations would be:
G=525-S
G=S+75
First Equation:
You can pick any value you like for S, for example: S=0 and then substitute it into the equation to get te first G-value:
G=525-0
so G=525.
So the first ordered pair would be (0,525)
You can do the same with a different S-value to get a second point to plot:
S=100
G=525-100
G=424
so the second ordered pair would be (100,424)
and now you can plot the points on the graph and connect them with a straight line.
See attached picture.
Second Equation:
The same procedure is followed for the second equation, in this case I used the same S-values, but you can use different values if you wish, so the two points to plot were:
(0,75)
(100,175)
and the graph looks like the one attached.
c)
In order to figure out how much each person earned, we need to find the point where the two graphs meet each other (see attached picture) in this case the point will be located at (225,300)
This means that Sharon earned a total of $225 while Geordi earned a total of $300.
S=$225 and G=$300
The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.
