Gemma had $2,054 in her checking account. She wrote a check for $584 to pay the rent on her apartment. After the landlord cashed
2 answers:
Answer:
Gemma have left $1,470 in her checking account.
Step-by-step explanation:
Given: Gemma had $2,054 in her checking account. She wrote a check for $584 to pay the rent on her apartment.
To find: After the landlord cashed the check, how much money did Gemma have left in her checking account?
Solution: To find the money Gemma have left in her checking account. After the landlord cashed the check, we need to subtract the amount she pays as the rent on her apartment from the money Gemma had in her checking account.
Gemma had $2,054 in her checking account.
She wrote a check for $584 to pay the rent on her apartment.
So, the amount Gemma have left in her checking account after the landlord cashed the check
Hence, Gemma have left $1,470 in her checking account.
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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).