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15 May, 03:03

The lifetime of an LED in a certain application is normally distributed with a mean μ = 25,000 hours and a standard deviation σ = 1500 hours. a. What is the probability that a light bulb will last more than 24,000 hours?

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  1. 15 May, 03:19
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    0.7477

    Step-by-step explanation:

    The mean (X) = 25,000 hrs

    Standard deviation (σ) = 1500 hrs

    The probability that the light bulb lasts more than 24,000hrs is Pr (X˃24,000)

    Using Z-scores, Z = (X - μ) / σ

    For X = 24,000

    Z = (24,000 - 25,000) / 1500

    Z = - 1000/1500

    Z = - 0.667

    From the normal distribution table, Z = 0.667 = 0.2477

    Φ (Z) = 0.2477

    Recall that if Z is negative,

    Pr (X˃a) = 0.5 + Φ (Z)

    Pr (X˃24,000) = 0.5 + 0.2477

    = 0.7477
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