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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Maya 3 days 2021-09-15T03:17:19+00:00 1 Answer 0

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    2021-09-15T03:18:45+00:00

    Answer:

    (A) 170, (B) 0.667

    Step-by-step explanation:

    Solution

    From 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

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