1- A company produces electronic devices with a mean lifetime of 3 years and a standard
deviation of one month. If 33 devices are taken randomly, what is the probability that they have
an average lifetime of 2.6 years.
2- The heights of high school students follow a normal distribution with a mean of 165 cm and a
standard deviation of 4 cm. What is the probability that a random student will be:
(a) Shorter than 160 cm.
(b) Between 152 and 175 cm.
(c) Taller than 125 cm.
(d) If 25 students were selected randomly, what is the probability that their mean height will
fall between 170 and 173.
(e) If 30 students were randomly selected, what is the probability that at least 15 of them
being shorter than 160 cm.
3- A factory produces screws with mean length of 5 cm and a standard deviation of 0.2 cm. If
samples of size 100 are taken, find the length L such that only 1% of sample means exceed L.
4- A factory manufactures a specific type of widget. The manufacturing process is not perfect,
and each widget has a random number of flaws. The number of flaws per widget, 𝑋, is a random
variable with a mean of 𝜇 = 2 flaws and a standard deviation of 𝜎 = 1.5 flaws.
The quality control process is as follows: The factory ships widgets in large batches of size 𝑛.
For each flaw on a widget, the company incurs a cost of $0.10 for repairs and refinishing.
The company wants to determine a fixed cost, 𝑐, to add to the price of each widget to cover these
expected flaw-related expenses.
Use the Central Limit Theorem to determine 𝑐 such that for a batch of n=400 widgets, they are
95% certain that the total amount collected will cover the total flaw-related costs.
Hint: Find the expression of the total cost first.