Question

(a) To compute probobilities regarding the sample moan using the normal model, what size sample would be required?. A. Any sample size could be used B. The normal model cannot be used it the shape of the distribution is skewod right. C. The sample size needs to be less than of equal to 30 . D. The sample sire needs to be greater than of equal to 30 . (b) What is the probablity that a random sample of a=35 oil changes rocults in a sample mean tmo less inan 15 minules? The probabity is approximately (Reund to four decimal places as needed.) There is 410% chance of being at of below a mean of-ehange time of winules. (Round to one decimal place as needed)

Answer 1

The sample size needs to be greater than or equal to 30 for computing probabilities regarding the sample mean using the normal model. (b) The probability is approximately 0.4100, rounded to four decimal places, and there is a 41.0% chance of having a mean oil change time of less than 15 minutes.(a) The correct answer is D

Explanation:

(a) The requirement of a sample size greater than or equal to 30 stems from the Central Limit Theorem. This theorem suggests that, for sample sizes of 30 or more, the distribution of the sample mean becomes approximately normal, regardless of the shape of the population distribution. This normality allows for the application of the normal model in computing probabilities related to the sample mean.

(b) To calculate the probability of a sample mean less than 15 minutes for a random sample of size 35, we utilize the normal distribution and its associated probabilities. The 41.0% probability is obtained by finding the area under the normal curve below the value of 15 minutes. This probability signifies the likelihood of obtaining a sample mean of 15 minutes or less, providing valuable insights for decision-making and analysis in the context of oil change times.