2. A tire manufacturer believes that the tread life of ts snow tires can be desc
ID: 3041582 • Letter: 2
Question
2. A tire manufacturer believes that the tread life of ts snow tires can be described by a Normal model with a mean tread life of 32,000 miles give-or-take 2,500 miles tctionofcaewen 30,00amd 35,00 miles? b. What is the IQR for the tread lives? In a planning marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However the tire dealer doesn't want to take too big a risk. If the dealer is willing to give refunds to no more than 1 in 25 customers, for what mileage ought he then guarantee these tires to last? c.Explanation / Answer
Mean = 32000 miles
Standard normal = 2500miles
P(X < A) = P (Z < (A - mean) /standard deviation)
A) P(30000 < X < 35000) = P(X < 35000) - P(X < 30000)
= P(Z < (35000-32000)/2500) - P(Z < (30000-32000)/2500)
= P(Z < 1.2) - P(Z < -0.8)
= 0.8849 - 0.2119
= 0.6730
b) IQR = Q3 - Q1
P(X < Q3) = 0.75
P(Z < (Q3 - 32000)/2500) = 0.75
(Q3 - 32000)/2500 = 0.67
Q3 = 33675
Similarly
(Q1 - 32000)/2500 = -0.67
Q1 = 30325
IQR = 33675 - 30325
= 3350
c) Let A be the mileage for which he can guarantee
P(X < A) = 1/25 = 0.04
P(Z < (A - 32000)/2500) = 0.04
(A - 32000)/2500) = -1.75
A = 27625 miles
He should guarantee that the tires will last 27625 miles
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