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 and a standard deviation of 5.2 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 25 batteries.

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

What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

What proportion of the samples will have a mean useful life of more than 36 hours? (Round your z value to 2 decimal places and final answer to 4 decimal places.)

What proportion of the sample will have a mean useful life greater than 34.5 hours? (Round your z value to 2 decimal places and final answer to 4 decimal places.)

What proportion of the sample will have a mean useful life between 34.5 and 36 hours? (Round your z value to 2 decimal places and final answer to 4 decimal places.)