Respuesta :
Answer:
The mean of the sampling distribution of means for the 36 students is of 18.6 homework hours per week.
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.
In this question:
For the population, the mean is 18.6. So, by the Central Limit Theorem, the mean of the sampling distribution is also 18.6.
You can use the CTL(Central Limit Theorem) here.
The mean of the sampling distribution of means for the 36 students is 18.6
Given that:
- The number of hours per week that seniors spend on homework is approximately normally distributed with mean 18.6 and std. deviation 6.0
- Simple random sampling is done of 36 senior and the sample mean is calculated.
To find:
Mean of the sampling distribution of means for the 36 students.
What does Central Limit Theorem states?
There are many variants, but for this case, it states that:
If X is a normally distributed random variable with mean [tex]\mu[/tex]standard deviation [tex]\sigma[/tex] random sample taken with size n (large and large n) is approximately normally distributed (the more large n is, the more close to this normal distribution it tends to) with mean [tex]\mu[/tex] standard deviation [tex]\sigma[/tex].
Thus, the mean of means of random samples taken is given by mean of the original population, which is 18.6
Thus, the mean of the sampling distribution of means for the 36 students is 18.6
Learn more about central limit theorem here:
https://brainly.com/question/1563663
