An entrepreneur plans to sell 10,000 anti-gravity shoes at a price of$sper pair. It costs$mto manufacture a pair.

She promises the customers that any failed pair will be replaced (only once) by a brand new pair within the warranty period. The entrepreneur needs to determine the warranty period that will ensure at least a 20% profit (calculate profit based on total expenses). You are asked to determine the maximum warranty period, in whole months, that she could afford to offer.

A series of tests of 19 pairs (sampling) to estimate the Time-Of-Failure (TOF, in months) yields the data given in the attached document: 'shoes'.

1. Using mean-ranking method fit the data to normalpdf,log-normalpdf, andWeibullpdf
2. Determine in each of the cases in (a) its mean, mode, and median.
3. For eachpdf,determine the warranty period.

TOF Data:

18.5

5.6

22.5

16.3

14.2

15.5

18

14

23.8

4.4

18

13.1

22.2

2.1

12

20.7

4.7

1.3

18.5