Explore BrainMass

Explore BrainMass

    Normal Distributions and Curves

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    (a) Answer true or false to each of the following statements
    (i) Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.
    (ii) Two normal distributions that have the same standard deviation have the same shape, regardless of the relationship between the means.

    (b) Consider the following normal curves. Curve I (u=1.5, sigma=3), curve II (u=1.5, sigma = 6.2), curve III (u=2.7, sigma=3), and curve IV (u=0, sigma=1).
    (i) Which curve has the largest speed?
    (ii) Which curves are centered at the same place?
    (iii) Which curves have the same shape?
    (iv) Which curve is centered farthest to the left?
    (v) Which curve is the standard normal curve?

    (c) Sketch and determine the area under the standard normal curve that lies
    (i) To the left of -3.20
    (ii) To the right of 0.61
    (iii) Between 1.11 and 2.75
    (iv) Between -1.11 and -2.75
    (v) To the right of 3.2

    © BrainMass Inc. brainmass.com June 4, 2020, 4:00 am ad1c9bdddf
    https://brainmass.com/statistics/normal-distribution/normal-distributions-and-curves-545703

    Solution Preview

    a) (i) True
    (ii) True

    (b) (i) The curve with largest value of sigma has largest spread: Curve II (mu=1.5, sigma=6.2)
    (ii) Curve I and Curve II are centred at the same place : mu ...

    Solution Summary

    Corresponding to different conditions of mean and standard deviations, some of the problems related to the normal distribution are solved.

    $2.19

    ADVERTISEMENT