The Central Limit Theorem
The Sony Corporation produces a Walkman that requires two AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As a part of their testing program Sony tests samples of 25 batteries.
a. What can you say about the shape of the distribution of sample mean?
b. What is the standard error of the distribution of the sample mean?
c. What proportion of the samples will have a mean useful life of more than 36 hours?
d. What proportion of the sample will have a mean useful life greater than 34.5 hours?
Step by step method for computing probability based on central limit theorem is given in the answer.