Page 1 of 2 12 LastLast
Results 1 to 15 of 18

Math Help - Normal distribution

  1. #1
    Newbie depaulie10's Avatar
    Joined
    Apr 2010
    From
    Chicago
    Posts
    14

    Normal distribution

    Hi,

    I need help with the setup of this problem.

    The capacity for the elevator is 2500 kgs. Baseball players have weights that are normally distributed with a mean of 120 kgs and a standard dev. of 80 kgs. 25 baseball players get on the elevator. What is the likelihood that the cable will snap?

    I set it up as Z= (X-) / σ but what is X ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by depaulie10 View Post
    Hi,

    I need help with the setup of this problem.

    The capacity for the elevator is 2500 kgs. Baseball players have weights that are normally distributed with a mean of 120 kgs and a standard dev. of 80 kgs. 25 baseball players get on the elevator. What is the likelihood that the cable will snap?

    I set it up as Z= (X-) / σ but what is X ?
    X=100

    You could say that the average weight of 25 players is 25(120)
    and the standard deviation of weight for 25 players is 25(80) kg.

    then

    \frac{X-\mu}{\sigma}=\frac{25(100)-25(120)}{25(80)}=\frac{100-120}{80}

    which is similar to dealing with a smaller elevator of capacity 100kg for a single player.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie depaulie10's Avatar
    Joined
    Apr 2010
    From
    Chicago
    Posts
    14
    Thanks for your help. I understand that part so now am I just supposed to look up the Z-score? What do I look for then?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by depaulie10 View Post
    Thanks for your help. I understand that part so now am I just supposed to look up the Z-score? What do I look for then?
    You may be using Z-values that start at zero or a table of positive and negative z-values,

    as clearly in this case z is negative.

    In this example you are calculating the probability that Z is greater that your z-score.

    Hence, if you only have positive values of z, you need to find the probability
    that Z is less than the modulus of your z-score.

    Since the average weight of the 25 players exceeds the breaking strain of the cable,
    there is a more than 50 percent chance the cable will snap.

    You could also calculate z=\frac{120-100}{80}=0.25

    and look up the probability that Z\ \le\ 0.25

    which is about 0.6

    Z tables give you the probability of z being less than or equal to some z-score. the normal distribution is symmetrical about the mean,
    so there is flexibility in making calculations.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie depaulie10's Avatar
    Joined
    Apr 2010
    From
    Chicago
    Posts
    14
    Thanks so much. I emailed my professor regarding this problem but he was not helpful at all. It'll be a long semester but I appreciate the help!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by depaulie10 View Post
    Hi,

    I need help with the setup of this problem.

    The capacity for the elevator is 2500 kgs. Baseball players have weights that are normally distributed with a mean of 120 kgs and a standard dev. of 80 kgs. 25 baseball players get on the elevator. What is the likelihood that the cable will snap?

    I set it up as Z= (X-) / σ but what is X ?
    The random variable is W = X_1 + X_2 + .... + X_{25} where X_i ~ Normal (\mu = 120, \, \sigma = 80).

    You're expected to know that the sum of normal random variables is also a normal random variable: Sum of normally distributed random variables - Wikipedia, the free encyclopedia.

    You should therefore know that in this case, W ~ Normal (\mu = 25 \times 120 = ...., \, \sigma = \sqrt{25 \times 80^2} = ....).

    Use the distribution of W to calculate Pr(W > 2500).
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie depaulie10's Avatar
    Joined
    Apr 2010
    From
    Chicago
    Posts
    14
    Quote Originally Posted by mr fantastic View Post
    The random variable is W = X_1 + X_2 + .... + X_{25} where X_i ~ Normal (\mu = 120, \, \sigma = 80).

    You're expected to know that the sum of normal random variables is also a normal random variable: Sum of normally distributed random variables - Wikipedia, the free encyclopedia.

    You should therefore know that in this case, W ~ Normal (\mu = 25 \times 120 = ...., \, \sigma = \sqrt{25 \times 80^2} = ....).

    Use the distribution of W to calculate Pr(W > 2500).
    Ah, well now I'm confused because I don't recall anything about a random variable W in lecture. Is the above explanation by Archie not right then?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by depaulie10 View Post
    Ah, well now I'm confused because I don't recall anything about a random variable W in lecture. Is the above explanation by Archie not right then?
    W is just the name I have given the random variable defined by the sum of the other random variabls. If you don't like W, use Y or U or Fred. I would not have bothered to make my reply if I thought that the replies you had already got were correct.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie depaulie10's Avatar
    Joined
    Apr 2010
    From
    Chicago
    Posts
    14
    Well thanks. So how do I go on calculate Pr(W > 2500)...
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by depaulie10 View Post
    Well thanks. So how do I go on calculate Pr(W > 2500)...
    Haven't you been taught how to calculate probabilities from a normal distribution? What do your classnotes and textbook say about getting the z-value, using tables etc. (Is this the very first question about calculating probability from a normal distribution that you have ever tried?)
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie depaulie10's Avatar
    Joined
    Apr 2010
    From
    Chicago
    Posts
    14
    I took one statistics class 3 years ago. The class is econometrics and I have 8 pages of class notes that are not helpful and contain little in the form of valuable examples which is why I'm on here. I've spent hours on this homework trying to understand and at this point I'm just trying to work my way backwards since the professor has not responded to my emails either. I plan on going to a tutor on Monday but I want to see what it is that I need help with! Thanks for responding anyway.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by depaulie10 View Post
    I took one statistics class 3 years ago. The class is econometrics and I have 8 pages of class notes that are not helpful and contain little in the form of valuable examples which is why I'm on here. I've spent hours on this homework trying to understand and at this point I'm just trying to work my way backwards since the professor has not responded to my emails either. I plan on going to a tutor on Monday but I want to see what it is that I need help with! Thanks for responding anyway.
    Step 1: Z = \frac{X - \mu}{\sigma} or, since the normal variable is W in this case, Z = \frac{W - \mu}{\sigma}.

    Substitute the mean and the standard deviation of W into the above to calculate the z-value.

    Do that and then I will go to step 2.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Newbie depaulie10's Avatar
    Joined
    Apr 2010
    From
    Chicago
    Posts
    14
    Thanks.

    Z= W - 3000 / 400
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by depaulie10 View Post
    Thanks.

    Z= W - 3000 / 400
    You also need to substitute W = 2500. Therefore Z = -1.25.

    Step 2: Calculate Pr(Z > -1.25).

    Note that Pr(Z > -1.25) = Pr(Z < 1.25) using the symmetry of the normal distribution. Pr(Z < 1.25) is something you can look up in your standard normal distribution tables ....
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Newbie depaulie10's Avatar
    Joined
    Apr 2010
    From
    Chicago
    Posts
    14
    Which is 0.8944.
    Last edited by depaulie10; April 10th 2010 at 05:21 PM.
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 27th 2011, 01:08 PM
  2. normal distribution prior and posterior distribution proof
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 9th 2011, 06:12 PM
  3. Replies: 2
    Last Post: March 29th 2010, 02:05 PM
  4. Replies: 2
    Last Post: August 25th 2009, 10:39 PM
  5. Replies: 1
    Last Post: April 20th 2008, 06:35 PM

Search Tags


/mathhelpforum @mathhelpforum