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 34 hours and a standard deviation of 5.5 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 33.5 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 33.5 and 36 hours? (Round your z value to 2 decimal places and final answer to 4 decimal places.)

Answer 1

1. Shape of the distribution: The distribution is normal distributed. It has a bell shaped symmetric distribution.

2. Standard error of the distribution of the sample mean, =

3. Proportion of the samples that will have a mean life of more than 36 hours, P( > 36) =

4. Proportion of the samples that will have a mean life of more than 33.5 hours,P(>33.5)=

5. Proportion of the samples that will have a mean life between 33.5 and 36 hours, P(33.5<<36) =