Respuesta :
Answer:
approximately Normal with mean 0.35
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
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 [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A researcher reports that 80% of high school seniors would pass a driving test, but only 45% of high school freshmen would pass the same driving test.
This means that [tex]p_1 = 0.8, p_2 = 0.45[/tex]
Subtraction of Variable 1 by Variable 2:
By the Central Limit Theorem, the shape will be approximately normal.
The mean is the subtraction of the means of each proportion. So
[tex]p = p_1 - p_2 = 0.8 - 0.45 = 0.35[/tex]
So the correct answer is given by:
approximately Normal with mean 0.35
