Ask Question
20 September, 05:42

The manufacturer of an extended-life lightbulb claims the bulb has an average life of 12,000 hours, with a standard deviation of 500 hours. If the distribution is bell shaped and symmetrical, what is the approximate percentage of these bulbs that will last between 11,000 and 13,000 hours?

+4
Answers (1)
  1. 20 September, 08:43
    0
    95.44%

    Step-by-step explanation:

    Mean (μ) = 12000 hrs

    Standard deviation (σ) = 500 hrs

    Let X be a random variable which is a measure of the extended life of the light bulb.

    The probability that these bulbs will last between 11,000 and 13,000 hours = Pr (11000 ≤ X ≤ 13000)

    For normal distribution

    Z = (x - μ) / σ

    Pr[ (11000 - 12000) / 500 ≤ (x - μ) / σ ≤μ

    ≤ (13000 - 12000) / 500]

    = Pr (-1000/500 ≤ z ≤ 1000/500)

    = Pr (-2 ≤ z ≤ 2)

    Pr (-2 ≤ z ≤ 2) = Pr (-2 ≤ z ≤ 0) + Pr (0 ≤ z ≤ 2)

    By symmetry

    Pr (-2 ≤ z ≤ 0) = Pr (0 ≤ z ≤ 2)

    Therefore

    Pr (-2 ≤ z ≤ 2) = 2Pr (0 ≤ z ≤ 2)

    = 2 (0.4772)

    = 0.9544

    Pr (-2 ≤ z ≤ 2) = 0.9544*100

    = 95.44%
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “The manufacturer of an extended-life lightbulb claims the bulb has an average life of 12,000 hours, with a standard deviation of 500 hours. ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers