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

Answer: Given that,

Mean = 36500

Standard deviation = 5000

Numbers sold = 1000

Total refund = 2586

Nos Sold	Mileage	Count(if Mileage < 30000)	Refund
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	3995	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

a) Average cost of promotion = 2.59

b) number of time paid > 25 = 42.0

Number of time refund paid = 91

Probability of paying more than 25 = 0.04