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2. A tire manufacturer believes that the tread life of its snow tires can be des

ID: 3042042 • Letter: 2

Question

2. A tire manufacturer believes that the tread life of its snow tires can be described by a Normal model with a mean tread life of 32,000 miles give-or-take 2,500 miles.

a.Approximately what fraction of these tires can be expected to last between 30,000 and 35,000 miles

b.What is the IQR for the tread lives?

c.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?

Explanation / Answer

a)

b)

for IQR ; z score = -/+ 0.6745

therefore IQR =2*0.6745*std deviation =2*0.6745*2500=3372.5

c)for 1/25 =0.04 ; at 4 pecentile z score =-1.75

therefore corresponding value =mean +z*std deviation =32000-1.75*2500=27625

for normal distribution z score =(X-)/ here mean=       = 32000.000 std deviation   == 2500