Ask Question
24 October, 20:46

The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.75 minutes. a. After observing 150 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 95% confidence interval for the mean assembly time.

+2
Answers (1)
  1. 24 October, 20:57
    0
    (15,595, 16,805)

    Step-by-step explanation:

    We have to:

    m = 16.2, sd = 3.75, n = 150

    m is the mean, sd is the standard deviation and n is the sample size.

    the degree of freedom would be:

    n - 1 = 150 - 1 = 149

    df = 149

    at 95% confidence level the t is:

    alpha = 1 - 95% = 1 - 0.95 = 0.05

    alpha / 2 = 0.05 / 2 = 0.025

    now well for t alpha / 2 (0.025) and df (149) = t = 1,976

    the margin of error = E = t * sd / (n ^ (1/2))

    replacing:

    E = 1,976 * 3.75 / (150 ^ (1/2))

    E = 0.605

    The 95% confidence interval estimate of the popilation mean is:

    m - E
    16.2 - 0.605
    15,595
    (15,595, 16,805)
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers