Respuesta :
Answer:
a) 1.34
b) 0.11
Step-by-step explanation:
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.
Population:
Mean is 5.10, standard deviation is 1.34
a. mean of the sampling distribution =
By the Central Limit Theorem, the mean of the sampling distribution is 5.1
b. standard deviation of the sampling distribution =
n = 150
By the Central Limit Theorem
[tex]s = \frac{1.3401}{\sqrt{150}} = 0.11[/tex]
