Homework: Assignment 06 Save Score: 0.67 of 1 pt 8 of 16 (12 complete) Hw Score:

Question

Homework: Assignment 06 Save Score: 0.67 of 1 pt 8 of 16 (12 complete) Hw Score: 56.67%, 9.07 of 16 pt Section 7.4 Exercise 15 Question Help For a new type of tire, a racing car team found that tire mleage is independent and follows a Normal model the average distance a set of tires would run during a race is 165 miles, with a standard deviation of 12 miles. Assume a) If the team plans to change tires twice during a 500-mile race, what is the expected value and standard deviation of miles remaining ater two changes? What is the probability they won't have to change tires a third time before the end of a 500 mile race? COLLEGE The City University of New York

Explanation / Answer

Mean = 165

std. deviation = 12

Thus, possible range of 1 tire = 165+- 12 i.e. (153 to 177 miles)

a)

expected distance by two tires combined = 165*2 = 330

Expected distance left from 500 miles = 500-330 = 170

Standard deviation = 12+!2 =24 (as range can be 153*2=306 to 177*2=354)

b)

P(that they wont change third tire by 500 miles)

Worst case 153*3 = 459

Best case = 177*3 = 531

Range = 531-459 = 72

Range for not replacing 3rd tire till 500 miles = 531-500 =31

Thus required probability = 31/72 = 0.43

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