Question

Suppose that engineers at porsche endeavor (at some point in the future) to verify the accuracy of 's claim that the average lifespan of a porsche is 10.6 years. given a sample of size 100 drawn from an exp(1/10.6) distribution, what does the central limit theorem say about the sample mean ത? is it normal or approximately normal? what would be its mean and standard deviation?

Answer 1

The Central Limit Theorem states that the sample mean of the average lifespan of a Porsche is approximately normal and has a mean of 10.6 years and a standard deviation of 1.06 years.

Step-by-step explanation:

The Central Limit Theorem states that if samples of sufficient size are drawn from a population, the distribution of sample means will be approximately normal, even if the population distribution is not normal. In this case, the sample mean is the average lifespan of a Porsche, and we are given that the sample is drawn from an exponential distribution with a mean of 10.6 years. Therefore, the sample mean is approximately normal. The mean of the sample mean is equal to the mean of the original distribution, which is 10.6 years. The standard deviation of the sample mean, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size, which is 1/√100. Therefore, the standard deviation of the sample mean is 1.06 years.