Question

(All answers were generated using 1,000 trials and native Excel functionality.)

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5,000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

(a)	For each tire sold, what is the average cost of the promotion?
	Round your answer to two decimal places.
	$_____
(b)	What is the probability that Grear will refund more than $25 for a tire?
	Round your answer to a one decimal percentage place.
	%_____

Answer 1

Mean	36500	Nos sold	1000	a) Avg. cost of promotion	2.59
Std Dev	5000	Total Refund	2586	b) Nos. of time paid > 25	42.00
				Nos. of time refund paid	91
Nos. Sold	Mileage Obtained	Count (if Mileage < 30000)	Refund	Probability of paying more than 25	0.04
1	40245	0	0
2	46024	0	0
3	31329	0	0
4	41139	0	0
5	35537	0	0
6	37546	0	0
7	32960	0	0
8	50738	0	0
9	30014	0	0
10	38109	0	0
11	38109	0	0
12	37713	0	0
13	32966	0	0
14	42770	0	0
15	39258	0	0
16	37823	0	0
17	30748	0	0
18	34231	0	0
19	42239	0	0
20	34029	0	0
21	45585	0	0
22	35812	0	0
23	37376	0	0
24	33069	0	0
25	35011	0	0
26	30874	0	0
27	32896	0	0
28	43331	0	0
29	35332	0	0
30	35167	0	0
31	30908	0	0
32	41910	0	0
33	39955	0	0
34	41129	0	0
35	35686	0	0
36	34693	0	0
37	35416	0	0
38	40859	0	0
39	28295	1	17
40	33560	0	0
41	36966	0	0
42	42888	0	0
43	37611	0	0
44	30522	0	0
45	48095	0	0
46	33468	0	0
47	35617	0	0
48	47102	0	0
49	36527	0	0
50	40011	0	0
51	39727	0	0
52	26770	1	32
53	39907	0	0
54	31925	0	0
55	34865	0	0
56	33228	0	0
57	36885	0	0
58	25614	1	44
59	30884	0	0
60	37481	0	0
61	28897	1	11
62	39598	0	0
63	34527	0	0
64	33236	0	0
65	27062	1	29
66	35418	0	0
67	36800	0	0
68	34504	0	0
69	39512	0	0
70	41992	0	0
71	31249	0	0
72	27422	1	26
73	34490	0	0
74	37314	0	0
75	41138	0	0
76	26604	1	34
77	40845	0	0
78	46486	0	0
79	32051	0	0
80	36307	0	0
81	25688	1	43
82	42045	0	0
83	38099	0	0
84	38299	0	0
85	38744	0	0
86	29798	1	2
87	35869	0	0
88	34052	0	0
89	28877	1	11
90	36811	0	0
91	38115	0	0
92	27160	1	28
93	47768	0	0
94	41700	0	0
95	40264	0	0
96	33387	0	0
97	48878	0	0
98	39884	0	0
99	36485	0	0
100	33487	0	0

Further simulations done for another 900 trials