Question

An office has 4 panasonic 6 brother and 3 HP printers. it is known that time before major printer failure is normally distributed with means 60, 80, and 85 days for panasonic, brother, and hp brands respectively. the standard deviation of time before major failure are 10, 10 and 12 days, respectively for the said brands.

A. Five printers are selected at random. what is the probability that at most 2 brother printers are chosen?

B. what is the expected time before failure of each printer?

C. A panasonic printer is chosen. What is the probabikity that it lasts more than 70 days before a major failure occurs?

D. three printers--- one of each brand---are selected. what is the probability that all these 3 printers fail before 85 days?

Answer 1

A. Five printers are selected at random. what is the probability that at most 2 brother printers are chosen?

Total printers = 13

Total brother printers = 6

0/6*7/13 + 1/6*7/13 + 2/6*7/13 = 0.2692

B. what is the expected time before failure of each printer?

The expected time before failure for Panasonic printer = 60

The expected time before failure for Brother printer = 80

The expected time before failure for HP printer = 85

C. A panasonic printer is chosen. What is the probabikity that it lasts more than 70 days before a major failure occurs?

P(x > 70) = (70 - 60)/10 = 1

The probability that it lasts more than 70 days before a major failure occurs is 0.1587.

D. three printers--- one of each brand---are selected. what is the probability that all these 3 printers fail before 85 days?

For Panasonic printer:

P(x < 85) = (85 - 60)/10 = 2.5

The probability is 0.9938.

For Brother printer:

P(x < 85) = (85 - 80)/10 = 0.5

The probability is 0.6915.

For HP printer:

P(x < 85) = (85 - 85)/12 = 0

The probability is 0.5.