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Euro Watch Company Report

1 ) The Euro Watch Company assembles expensive wristwatches and then sells them to retailers throughout Europe. The watches are assembled with two assembly lines with below specification:

Line 1:

Old equipment

Less reliable

Defect rate of 2%

Capacity: 500 watches per hour

Line 2:

New equipment

More reliable

Defect rate of 1%

Capacity: 500 watches per hour

We need to find the smallest number of defected watches each line produces independently in a given hour with success rate of 99%

The distribution is a binomial distribution since we have 500 independent and identical trials with a certain probability of success and we see a defected or non- defected option therefore in the excel file we should use the command BINOMDIST. Number of trials is 500 and for cumulative we should consider 1 as we want to have the probability of less than or equal to K defects.

As we can see in below tables the smallest defected number that reaches the rate of 99% is 18 watches for line 1 and 11 defected for line 2, which is obvious since line 2 is newer, and with lower defect rate.

￼￼￼line 2 99% 1% 500

Line 2

Line ￼ line 1

￼Defect-free 98%

￼Defective 2%

￼Made watches per hour 500

￼￼Defected amount (k) Line 1 Defected amount (k)

0 0.0000

1 0.0005

2 0.0026

3 0.0098

4 0.0281

5 0.0652

6 0.1276

7 0.2175

8 0.3305

9 0.4567

10 0.5830

11 0.6979

12 0.7935

13 0.8667

14 0.9186

15 0.9530

16 0.9743

17 0.9866

18 0.9934

19 0.9969

20 0.9986

21 0.9994

22 0.9998

23 0.9999

24 1.0000

25 1.0000

26 1.0000

27 1.0000

28 1.0000

29 1.0000

30 1.0000

0

1

2

3

4

5

6

7

8

9

10

11 ￼ 0.9948

12

13

14

15

16

17

18

19

20

0.9981 0.9994 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0066 0.0398 0.1234 0.2636 0.4396 0.6160 0.7629 0.8677

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