Show all work. Be sure to label diagrams (must show even distribution graph with

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

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