Show all work. Be sure to label diagrams (must show even distribution graph with
ID: 3363290 • Letter: S
Question
Show all work. Be sure to label diagrams (must show even distribution graph with labels for each section) and include your probability and calculator statements.
2 – The amount of time an iPhone battery lasts before it fails is normally distributed with a mean 5.2 years and a standard deviation of 1.3 years.
a - Find the probability that a randomly selected iPhone will have a battery that dies within three years of purchase.
b - If Apple sold 150,000 of iPhones this week, how many would they expect to get back if they offer a 2 year warranty?
c - What is the maximum lifetime of the lowest 10% of iPhone batteries?
Explanation / Answer
a) z = (3 - 5.2)/1.3
z = - 0.733
P = 0.2327
b) z = (2 - 5.2)/1.3
z = - 2.46
P = 0.006947
Get back = 150000 * 0.006947
Get back = about 1042
c) z score for lowest 10% = - 1.28
(x - 5.2)/1.3 = - 1.28
x = 3.536