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3 August, 23:51

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. what is the probability that a tire lasts between 54,000 and 66,000 miles?

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  1. 4 August, 00:29
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    To solve for the P (54,000≤x≤66000) we proceed as follows:

    z-score = (x-μ) / σ

    μ-60000

    σ-4000

    thus:

    when x=66,000

    z-score = (66000-60000) / 4000=1.5

    P (z≤1.5) = 0.9332

    when x=54000

    z = (54000-60000) / 4000

    z=-1.5

    P (z≤-1.5) = 0.0668

    thus

    P (54,000≤x≤66000)

    =P (z≤1.5) - P (z≤-1.5)

    =0.9332-0.0668

    =0.8664

    Answer: 0.8664
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