Question

the shape of the distribution of the time required to get an oil change at a 10 - minute oil - change facility is skewed right. however, records indicate that the mean time is 11.1 minutes, and the standard deviation is 3.3 minutes. complete parts (a) through (c). (a) to compute probabilities regarding the sample mean using the normal model, what size sample would be required? ○ a. the sample size needs to be less than or equal to 30. ○ b. any sample size could be used. ○ c. the normal model cannot be used if the shape of the distribution is skewed right. ○ d. the sample size needs to be greater than or equal to 30.

Explanation:

The Central Limit Theorem states that for a non - normal population (in this case, the distribution of oil - change times is skewed right), the sampling distribution of the sample mean \(\bar{X}\) is approximately normal if the sample size \(n\) is large enough. A common rule of thumb is that \(n\geq30\) (when the population is non - normal) for the sampling distribution of the sample mean to be approximately normal.

Answer:

D. The sample size needs to be greater than or equal to 30.