Question

The shape of the distribution of the time required to get an oil change at a 10-minute oil change facility is unknown. However, records indicate that the mean time is 112 minutes, and the standard deviation is not provided.

(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. The normal model cannot be used if the shape of the distribution is unknown.
C. Any sample size could be used.
D. The sample size needs to be greater than or equal to 30.

Answer 1

To use the normal model for sample mean probabilities, the Central Limit Theorem suggests a sample size of greater than or equal to 30 is necessary, regardless of the population distribution's shape.

Step-by-step explanation:

To compute probabilities regarding the sample mean using the normal model, the Central Limit Theorem (CLT) needs to be taken into account. The CLT states that, if the sample size is large enough, the distribution of the sample mean will be approximately normal regardless of the shape of the population distribution. This is usually the case when the sample size is greater than or equal to 30. Therefore, the correct answer is D. The sample size needs to be greater than or equal to 30. For distributions such as the uniform distribution or the normal distribution, with known parameters such as mean and standard deviation, specific formulas and methods like the normalcdf function can be used to calculate probabilities directly.