Question

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 21.3 minutes, and the standard deviation is 3.2 minutes. compute parts (a) through (c) below.
(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. the sample size needs to be greater than 30.
c. the sample size needs to be less than 30.
d. any sample size could be used

Explanation:

The problem is about using the normal model for sampling distributions. When the original distribution is skewed right, the Central Limit Theorem (CLT) states that for the sampling distribution of the sample mean to be approximately normal, the sample size should be sufficiently large (usually \( n \geq 30 \)). So if the original distribution is skewed right, we need a sample size greater than 30 to use the normal model for probabilities related to the sample mean. Option B states "The sample size needs to be greater than 30", which aligns with the CLT requirements for skewed populations. Option A is incorrect because the normal model can be used with large enough samples even if the original is skewed. Option C is incorrect as a sample size less than 30 won't ensure normality for a skewed distribution. Option D is incorrect because the sample size does matter for skewed distributions.

Answer:

B. The sample size needs to be greater than 30.