Assignment:
Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.6 hours. As a part of their testing program Sony tests samples of 9 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? (Round your answer to 4 decimal place.)
(c) What proportion of the samples will have a mean useful life of more than 37 hours? (Round your answer to 4 decimal place.)
(d) What proportion of the sample will have a mean useful life greater than 33 hours? (Round your answer to 4 decimal place.)
(e) What proportion of the sample will have a mean useful life between 33 and 37 hours? (Round your answer to 4 decimal place.)
Provide complete and step by step solution for the question and show calculations and use formulas.