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15 March, 19:42

Suppose a brand of light bulbs is normally distributed, with a mean life of 1300 hr and a standard deviation of 50 hr. Find the probability that a light bulb of that brand lasts between 1225 hr and 1365 hr.

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  1. 15 March, 19:58
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    Step-by-step explanation:

    Since the life of the brand of light bulbs is normally distributed, we would apply the the formula for normal distribution which is expressed as

    z = (x - u) / s

    Where

    x = life of the brand of lightbulbs

    u = mean life

    s = standard deviation

    From the information given,

    u = 1300 hrs

    s = 50 hrs

    We want to find the probability that a light bulb of that brand lasts between 1225 hr and 1365 hr. It is expressed as

    P (1225 ≤ x ≤ 1365)

    For x = 1225,

    z = (1225 - 1300) / 50 = - 1.5

    Looking at the normal distribution table, the probability corresponding to the z score is

    0.06681

    For x = 1365,

    z = (1365 - 1300) / 50 = 1.3

    Looking at the normal distribution table, the probability corresponding to the z score is

    0.9032

    Therefore

    P (1225 ≤ x ≤ 1365) = 0.9032 - 0.06681 = 0.8364
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