Ask Question
24 February, 21:53

A company manufactures light bulbs. The lifetime for these bulbs is 4,000 hours with a standard deviation of 200 hrs. What lifetime should the company promote for these bulbs, so that only 2% of them burnout before the claimed lifetime?

+3
Answers (1)
  1. 24 February, 22:06
    0
    The company should promote a lifetime of 3589 hours for these bulbs, so that only 2% of them burnout before the claimed lifetime.

    Step-by-step explanation:

    Consider the lifetime of light bulbs is normally distributed. Then, μ = 4000 hours and σ = 200 hours.

    Let X be the lifetime of bulbs. We need to find the lifetime before which only 2% (0.02) of the bulbs burn out. Suppose the value of this lifetime is y. then, we need to find out P (X
    We will use the z-score formula:

    z = (x-μ) / σ

    P (X
    P ((X-μ) / σ < (y-μ) / σ) = 0.02

    P (z < (y-4000) / 200) = 0.02

    We can find the value of z at which the probability is 0.02 from the normal distribution (areas under the normal curve) table.

    From the table we can see that 0.02 lies between z values - 2.05 and - 2.06. So,

    z = [-2.05 + (-2.06) ]/2

    = - 4.11/2

    z = - 2.055

    So,

    (y-4000) / 200 = - 2.055

    y-4000 = - 411

    y = 4000 - 411

    y = 3589 hours

    The company should promote a lifetime of 3589 hours for these bulbs, so that only 2% of them burnout before the claimed lifetime.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A company manufactures light bulbs. The lifetime for these bulbs is 4,000 hours with a standard deviation of 200 hrs. What lifetime should ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers