20 cubic inches of a gas with an absolute pressure of 5 psi is compressed until its pressure reaches 10 psi. What's the new volu
2 answers:
It is given that that initial volume of gas is 20 cubic inches.
The initial pressure is given as 5 psi.
The final pressure is given as 10 psi
We are asked to calculate the final volume.
Let initial and final volume of gas is denoted as
Let the initial and final pressure of gas is denoted as
As per the question the temperature of a gas is constant.
From Boyle's law we know that pressure of a given mass of a gas is inversely proportional to the applied volume at constant temperature.
Hence mathematically
Putting the values of these respective quantities as mentioned above we get-
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Answer:
a. μ 3 ± 1.8 = [1.2,4.8]
b. The correct answer is option D. No, because the sample size is large enough.
Explanation:
a. The population mean can be determined using a confidence interval which is made up of a point estimate from a given sample and the calculation error margin. Thus:
μ±(t*s)/sqrt(n)
where:
μ = is the 95% confidence interval estimate
x_ = mean of the sample = 3
s = standard deviation of the sample = 5.8
n = size of the sample = 41
t = the t statistic for 95% confidence and 40 (n-1) degrees of freedom = 2.021
substituting all the variable, we have:
μ 3 ± (2.021*5.8)/sqrt(41) = 3 ± 1.8 = [1.2,4.8]
b. The correct answer is option D. No, because the sample size is large enough.
Using the the Central Limit Theorem which states that regardless of the distribution shape of the underlying population, a sampling distribution of size which is ≥ 30 is normally distributed.