The shape of the distribution of the time required to get an oil change at a 20 -minute oil-change facility is skewed right. However, records indicate that the mean time is 21.1 minutes, and the standard deviation is 3.9 minutes. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? Choose the required sample size below. A. The normal model cannot be used if the shape of the distribution is skewed right. B. Any sample size could be used. C. The sample size needs to be greater than 30 . D. The sample size needs to be less than 30 .
Solution
Step 1 ：The question is asking for the sample size required to compute probabilities regarding the sample mean using the normal model, given that the distribution of the time required to get an oil change at a 20-minute oil-change facility is skewed right.
Step 2 ：The Central Limit Theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is large enough (usually n > 30).
Step 3 ：Therefore, the sample size needs to be greater than 30.
Step 4 ：\(\boxed{\text{C. The sample size needs to be greater than 30}}\)
