Respuesta :
Answer:
The distribution of average life time is approximately normallyl distributed with mean 20 hours and standard deviation of 0.4743 hours
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.
In this problem
[tex]\mu = 20, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743[/tex]
The distribution of average life time is approximately normallyl distributed with mean 20 hours and standard deviation of 0.4743 hours
