Tires are among the most commonly replaced parts on vehicles. They are not cheap and shopping for them is confusing. When we look for tires, many of us pay attention to the warranty that accompanies them as a way of getting reliable and long-lasting tires - sometimes paying a hefty premium for high performance.

Tire manufacturers test their tires in house. Tires are inflated to the optimal pressure and then the tires spin on specially designed treadmills.

The thread-life warranties are presented in a mileage estimate. If a tire has worn out evenly across the tread well before its estimated mileage limit, it may qualify for replacement.

Of course, the tire manufacturer would like to minimize warranty replacements by making sure that their tires meet the mileage standard. To this end, the production manager of a tire company is testing their mileage warranty of 30,000 miles. To do the test, 60 tires are put through the treadmill test. When the tires are worn down to the 2/32nd thread-wear indicators, the mileage is recorded. You have the result of one such sample in the fileTire_Mileage.xlsxDownload Tire_Mileage.xlsx

I provide you with the following to give you some help so you can focus on the last 3 questions: thelowerbound of the 95% confidence interval of the mean mileage for the tires is: 29,489.94 the upper bound of the 95% confidence interval of the mean mileage for the tires is: 30,781.59 the probability of finding a sample with a mean of less than 30,000 miles is:

0.337 "" Question: What is the required sample size, if the management wants to be within 250 miles of the actual population mean? "" "The Tire Mileage" is:

Tire #	Mileage
1	31564
2	27886
3	28822
4	27326
5	31535
6	31880
7	28376
8	29664
9	25001
10	34981
11	32048
12	27672
13	31267
14	31512
15	35228
16	25089
17	32372
18	29749
19	28670
20	34683
21	34551
22	32811
23	30535
24	26741
25	30874
26	27535
27	28444
28	27504
29	30179
30	31491
31	28531
32	29715
33	30103
34	33841
35	28462
36	27535
37	34548
38	27165
39	28906
40	32027
41	31802
42	31878
43	31972
44	30650
45	31514
46	27820
47	34669
48	30534
49	30598
50	29459
51	28559
52	28630
53	33827
54	26831
55	28394
56	27616
57	29207
58	30024
59	29883
60	27456