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10 January, 14:52

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of at least 30,000 miles

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  1. 10 January, 14:58
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    Probability of (x > 30,000) = 0.97725

    Explanation:

    Given:

    Mean distribution (μ) = 40,000

    Standard deviation (σ) = 5,000

    Raw score of x = 30,000

    Computation:

    Probability (x > 30,000) = Probability [z > (Raw score of x - Mean distribution) / Standard deviation]

    Probability (x > 30,000) = Probability [z > (30,000 - 40,000) / 5,000]

    Probability (x > 30,000) = Probability [z > 2]

    Using Z score calculator:

    Probability of (x < 30,000) = 0.02275

    So, Probability of (x >30,000) = 1 - 0.02275

    Probability of (x > 30,000) = 0.97725
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