Atire company has developed a new type of steel-belted radial tire.Extensive tes
ID: 2953694 • Letter: A
Question
Atire company has developed a new type of steel-belted radial tire.Extensive testing indicates that the population of lifetimesobtained by all tires of this new type is normally distributed witha mean of 65,000 km and a standard deviation of 6,500 km.a) the company wishes to offer a guarantee that providess adiscount on a new set of tires if the original tires purchases donot exceed the lifetime stated in the guarentee. What should theguarenteed lifetime be if the tire company desires that no morethan 2% of the tires will fail to meet the guarenteedlifetime?
b) if a random sample of 12 of the new type of tire are tested,what is the probability that at least 2 of them will last longerthan 75,000 km?
Explanation / Answer
F is standard normal function F(x-65000/6500) = 0.02 (x-65000)/6500 = F^-1(.02)= -2.05 from the table (http://training.ce.washington.edu/wsdot/… =>x-65000= -13325 =>x= 51675 km so the company must give a guarantee of 51675 km b) (p>75000) =1- F((75000-65000)/6500) = 1-F(1.53)(get the valefrom table)= 1-0.937=.063 P at-least 2 will last = 1- (probability none will last +probability one will last) =>1- (12C0*(.937)^12+12C1*(.937)^11*.063) =>1- (.45+.369) =>1-.819 = 0.18
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