Question

Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 35 hours. hours and a standard deviation of 5.2 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 25 batteries.

a. What can you say about the shape of the distribution of the sample mean?

Answer 1

The distribution of the sample mean for the battery life of AA batteries produced by Power +, Inc. is approximately normal.

Step-by-step explanation:

The shape of the distribution of the sample mean can be described as approximately normal. When the sample size is large enough (n > 30) and the population is normally distributed, the distribution of the sample mean will follow a normal distribution regardless of the shape of the population distribution. This is known as the Central Limit Theorem.

In this case, Power +, Inc. is testing samples of 25 batteries. Since the sample size is 25, which is less than 30, we need to check if the population is normally distributed. Since the population of battery lives follows a normal distribution, as stated in the question, we can conclude that the distribution of the sample mean will also be approximately normal.