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(All answers were generated using 1,000 trials and native Excel functionality.) Grear Tire Company has produced a...

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Basic Math

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

Grear Tire Company has produced a new tire with an estimatedmean lifetime mileage of 36,500 miles. Management also believesthat the standard deviation is 5,000 miles and that tire mileage isnormally distributed. To promote the new tire, Grear has offered torefund some money if the tire fails to reach 30,000 miles beforethe tire needs to be replaced. Specifically, for tires with alifetime below 30,000 miles, Grear will refund a customer $1 per100 miles short of 30,000.

(a)For each tire sold, what is theaverage cost of the promotion?
Round your answer to two decimalplaces.
$
(b)What is the probability that Grearwill refund more than $25 for a tire?

Round your answer to a one decimal percentage place.

Answer & Explanation Solved by verified expert
4.3 Ratings (634 Votes)

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
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