Provide an appropriate response.
-Furnace repair bills are normally distributed with a mean of 271 dollars and a standard deviation of 15 dollars. If 36 of these repair bills are randomly selected, find the probability that they have a mean cost between 271 dollars and 273 dollars.
A) $0.2881$
B) $0.7881$
C) $0.2119$
D) $0.5517$

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we calculate the probability of the sample mean being between 271 and 273 dollars. The z-score for 271 is (271-271)/15/√36 = 0, and for 273 it is (273-271)/15/√36 = 2/15*6 = 0.8. Looking up these z-scores in the standard normal distribution table, the probability of being between these two values is approximately 0.2881.

Provide an Appropriate Response 0.28810.28810.2881 B) 0.78810.78810.7881 C) 0.21190.21190.2119 D) 0.55170.55170.5517

Provide an Appropriate Response $0.2881$ B) $0.7881$ C) $0.2119$ D) $0.5517$