The lifetimes of light bulbs of a particular type have mean =1,320 hours and standard deviation =180 hours. A consumer advocacy organization, interested in investigating the reliability of the light bulbs, decides to measure the lifetimes of 100 randomly chosen bulbs. Let Y denote the sample mean lifetime of the 100 bulbs measured in hours.

What is the expected value of Y , i.e., what is E (Y )?

What is the standard deviation of Y , i.e., what is SD (Y ) ?

If the units of measurement for Y were changed from hours to days, how would your answers to questions 2 and 3 change, i.e., what values would E (Y ) and

Var (Y ) take?

By using the central limit theorem, approximate the probability that the sample average Y is between 1,300 and 1,350 hours, i.e., approximate P(1,300Y 1,350).

If the lifetimes of the light bulbs were assumed to be normally distributed, what is the probability that a randomly chose light bulb has lifetime between 1,300 and 1,350 hours?