## For a new type of tire, a racing car team found the average distance a set of tires would run during a race is 165 miles, with a standard

Question

For a new type of tire, a racing car team found the average distance a set of tires would run during a race is 165 miles, with a standard deviation of 15 miles. Assume that tire mileage is independent and follows a Normal model. 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 after two changes? b) What is the probability they won’t have to change tires a third time (and use a fourth set of tires) before the end of a 500 mile race?

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Math
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2021-09-15T03:17:19+00:00
2021-09-15T03:17:19+00:00 1 Answer
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## Answers ( )

Answer:(A) 170, (B) 0.667

Step-by-step explanation:SolutionFrom the question given, we solve for both A and B

Let X represent the distance a set of tires would run during a race.

Now,

(a) E ( Miles left ) = 500 – (2μ)

= 500 – ( 2* 165) = 170

Standard deviation (SD) (Miles remaining) = 2σ/√2 = 2 * 15/√2

= 21.215

(b) P [X≥ E (Miles remaining)] = P (X≥ 170)

= 1 -P (X< 170)

= 1- P = (X -μ /σ < 170 – μ/σ)

= 1- P ( Z < 170 – 165/15)

=1 – P (Z< 0.3333)

= 0.667