Ask Question

The random variable X is normally distributed with mean 82 and standard deviation 7.4. Find the value of q such that P (82 - q < X < 82 + q) = 0.44.

+3
Answers (1)
  1. 4 May, 18:11
    0
    P (82 - q < x < 82 + q) = 0.44

    P (x < 82 + q) - P (82 - q) = 0.44

    P (z < (82 + q - 82) / 7.4 - P (z < (82 - q - 82) / 7.4) = 0.44

    P (z < q/7.4) - P (z < - q/7.4) = 0.44

    P (z < q/7.4) - (1 - P (z < q/7.4) = 0.44

    P (z < q/7.4) - 1 + P (z < q/7.4) = 0.44

    2P (z < q/7.4) - 1 = 0.44

    2P (z < q/7.4) = 1.44

    P (z < q/7.4) = 0.72

    P (z < q/7.4) = P (z < 0.583)

    q/7.4 = 0.583

    q = 0.583 x 7.4 = 4.31
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The random variable X is normally distributed with mean 82 and standard deviation 7.4. Find the value of q such that P (82 - q < X < 82 + ...” 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