If x= -3, and -3 = y, then what can be said about the relationship between x and y? Explain
2 answers:
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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:
The value of n = 4 and
The value of x =
Step-by-step explanation:
Method I:
As given, 12x -20=n (3x-5) .........(1)
Firstly , take 12x - 20
As 12x - 20 can be written as 4(3x - 5)
∴ equation (1) becomes
4(3x - 5) = n (3x-5)
Divide the equation by (3x-5) , we get
4 = n
Method II:
As given, 12x -20=n (3x-5)
⇒12x - 20 = 3nx - 5n
⇒12x - 3nx = 20 - 5n
⇒3x(4 - n) = 5( 4 - n)
Divide the equation by (4-n) , we get
3x = 5
⇒ x =
∴ we get
n = 4 and x =
Now, check that value of n and x satisfies the equation or not
12() - 20 = 4( 3(
) - 5)
⇒4(5) - 20 = 4(5 - 5)
⇒20 - 20 = 4(0)
⇒ 0 = 0
Hence , we get
The values of x and n satisfies the equation
so, we get
n = 4 and x =
Answer:
$4.64
Step-by-step explanation:
1 cup = 16 tablespoons
cup = 8 tablespoons
Each lemon yields about 2 tablespoons of juice. You need 8 tablespoons for one lemon pie, so you need lemons for one pie and
lemons for two pies.
The store is selling lemons at $0.58 each, hence, 8 lemons will cost