Batteries for the most popular Electric Vehicles can last for an average of 12 hours before needing to be recharged, with a standard deviation of 5.1 hours. These follow a normal distribution. A random sample of 36 batteries were monitored to assess their performance. Based on the Central Limit Theorem, provide answers for the following.

i.) What is the variance, and standard error of the sampling distribution of the sample mean?

ii.) What is the probability that the sample mean is less than 11 hours?

iii.) What is the probability that the sample mean is more than 12.3 hours?

iv.) What is the probability that the sample mean is outside of the range of 11.5 to 12.5 hours?

v.) What is the practical significance of the Central Limit Theorem?