+ Reply to Thread
Results 1 to 5 of 5

Thread: Normal Distribution

  1. #1
    Points: 1,971, Level: 26
    Level completed: 72%, Points required for next Level: 29

    Posts
    11
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Normal Distribution




    An individuals’ heights are normally distributed with mean 70 and standard deviation 3 (inches).
    a) What proportion of the population is over 6 feet tall?
    For this question I used the formula z = X - mean / standard deviation.
    So, I got (X-70)/3. Then I multiplied 6 *12 to get 72 to match the inches, and then plugged it into the equation. 72-70/3= 2/3. Now, I am stuck as to what to do on how to find the proportion? Is the answer 2/3?

    b) If 75 percent of the population is taller than Mike, what is Mike’s height?
    I thought to use the same equation in a). So, it would be 1- 0.75= 0.25. 0.25 = (X-70)/3
    So, X = 70.75. Is that the correct height?
    Thanks for your time.

  2. #2
    TS Contributor
    Points: 12,501, Level: 73
    Level completed: 13%, Points required for next Level: 349

    Posts
    951
    Thanks
    0
    Thanked 103 Times in 100 Posts
    Do you know a table (in your book?) such as this:


    Use this table to get your answer. What you have calculated for part (a) is z = 2/3. You want to find P[Z > 2/3] (">" because the problem says "over 6 feet tall"). Note that this table gives you P[Z < z].

  3. #3
    Points: 1,971, Level: 26
    Level completed: 72%, Points required for next Level: 29

    Posts
    11
    Thanks
    0
    Thanked 0 Times in 0 Posts
    ok, I see, but why is there Z? What would Z be in this case? Cause z = 2/3, so that is a column or row?

  4. #4
    Points: 2,839, Level: 32
    Level completed: 60%, Points required for next Level: 61

    Location
    Leeds, UK
    Posts
    51
    Thanks
    4
    Thanked 0 Times in 0 Posts
    It's a column *and* a row ! The columns give the probabilities for the second decimal place of z.

    By way of example, P(Z<0.45) = 0.6736

    Note the comment by Mean Joe about ">" and also note that P(Z<0)=0.5

  5. #5
    Points: 1,971, Level: 26
    Level completed: 72%, Points required for next Level: 29

    Posts
    11
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Thanks for answering
    So, to get my answer would i have 1- P(Z<0.67), right?
    And, is my b) question right???

+ Reply to Thread

           




Similar Threads

  1. Replies: 2
    Last Post: 05-11-2011, 01:35 PM
  2. Is a subset of a normal distribution normal?
    By bordonbert in forum Probability
    Replies: 4
    Last Post: 10-29-2009, 03:54 AM
  3. Normal? Bimodal normal? Some other distribution?
    By statsCZ in forum Statistical Research
    Replies: 4
    Last Post: 01-28-2009, 08:31 AM
  4. approximating binomial distribution w/ normal distribution
    By fiddlestix327 in forum Probability
    Replies: 2
    Last Post: 06-25-2008, 06:45 PM
  5. Replies: 0
    Last Post: 01-23-2008, 11:32 PM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats