Question

Warranty for Alpha Tires 1. Introduction Alpha Tire Company wishes to offer a warranty for their tires. In order to perform an assessment of the tires' durability, a sample of 41 newly manufactured tires is selected at random. The mileage at which each tire will fail needs to be determined. Rather than driving the tires around for months until they fail naturally (field test), the tires are installed on a special machine that simulates wear and tear (lab test). The machine operates at high speed, high temperature, and applies high pressure on the tires against a rough surface. As a result, the tires blow up in just a few hours. A conversion formula is then used to compute each tire's simulated mileage. You are asked to advise Alpha Tire Co, on the feasibility of offering a 35,000-mile warranty on their tires. At this time Alpha Tire believes the mean time to failure is 40,000 miles (u=40,000) with standard deviation of miles to failure to be 3700 or (a +3700) 2. The data Tire mileage to failure data are provided in Excel file Case3 DATA. The file is posted on Canvas. 3. Sample Statistics in Excel Using Excel functions =average and Estdev(), compute the sample mean and the sample standard deviation. You may also use the DATA -DATA ANALYSIS....DESCRIPTIVE STATISTICS in Excel to obtain these statistics. Question #1: Assuming that the tire mileage is normally distributed with u = 40,000 miles and a known o =3,700 miles compute the probability that a randomly selected tire lasts less than the 35,000 promised by the warranty or we could ask what% would we expect to replace given this policy Question #2: Assuming that the tire mileage is normally distributed and the mean number of miles to failure is not known and a known 6 = 3,700 miles. Using your sample of 41 tires as your estimate of the mean (X Bar); what is the upper and lower bound of a 95% confidence interval? Question #3: Assuming that the tire mileage is normally distributed and the mean number of miles to failure is not known nor iso. Using your sample of 41 tires as your estimate of the mean (X Bar) and s-the sample standard deviation; what is the upper and lower bound of a 95% confidence interval? Remember you are estimating the sample standard deviation.

Answer 1

Pago No. and standard deviation Calculate mean using formula average (B2: 842) Staden.s (B2B42) 3949556 3783.29 ll = 40.000 = 3700 P(X235,000) PIX-u 35,ooo - 4o, boo 3700 PIZ -1.35) 0.08851 2) interval for mean is 951. confidence gonen oy - 5c I o Za Jn 39495.56 I 3700 x 1.96 Jul 39495.56 + 1132.5T (38362.99 40628.13) 3 95% confidence interval is given by- - + S tant 29445.56 3783.29 . * 2.02107 Jur 1194.15 40 689.71 ) | 39495-56 (38 301.

Date Page No. 3² 23 > 2 E2 = (3700)?x(1096) 2 (1000) 52.59 53 = m