Question 1 (5 marks)
Assume that a group of electronic devices whose lifetimes are i.i.d random variables. A technician wants to
use the sample mean to estimate the mean value of the lifetime. Further assume the standard deviation for
the lifetimes of an electronic device is 2 year.
(1.1) (3 marks) Use the Central Limit Theorem to approximate the number of electronic devices that the
technician should test, denoted as $n$, such that the sample mean is within 0.05 years of the actual mean with
probability greater than or equal to 96%.
(1.2) (2 marks) Suppose that the true mean of the lifetimes of a group of electronic devices is 8 years. Suppose
we average the lifetimes of 2500 electronic devices. What is the probability that the measured average is
within 0.05 years of the true mean?
