Results 1 to 3 of 3

Math Help - Normal Distribution and Standard Deviation

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    2

    Normal Distribution and Standard Deviation

    This is the question:
    Hermione runs a coaching college and gives all her students an exam at the end of the course. from past experience she knows that the results are normally distributed with a mean of 76.5% and standard deviation of 7.5%. the latest course has 2000 students and hermione offers to refund the cost of the course to any student who does not score a certain percentage.
    what should this percentage be if hermione is only prepared to refund 3 students?
    justify your answer with calculations and include at least ONE diagram in your solution.

    kk.. well ive got an answer with not much working and wonder if there is any more and i cannot find a diagram to use. can someone please help??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jan 2009
    Posts
    105
    Quote Originally Posted by scarybear12 View Post
    This is the question:
    Hermione runs a coaching college and gives all her students an exam at the end of the course. from past experience she knows that the results are normally distributed with a mean of 76.5% and standard deviation of 7.5%. the latest course has 2000 students and hermione offers to refund the cost of the course to any student who does not score a certain percentage.
    what should this percentage be if hermione is only prepared to refund 3 students?
    justify your answer with calculations and include at least ONE diagram in your solution.

    kk.. well ive got an answer with not much working and wonder if there is any more and i cannot find a diagram to use. can someone please help??
    You need the value of x* such that Pr(X < x*) = 3/2000. Use tables (or technology) to find the value of z* such that Pr(Z < z*) = 3/2000. Then Z = \frac{X - \mu}{\sigma} \Rightarrow z* = \frac{x* - 76.5}{7.5}. Substitute the value of z* and solve for x*.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,720
    Thanks
    1472
    Quote Originally Posted by scarybear12 View Post
    This is the question:
    Hermione runs a coaching college and gives all her students an exam at the end of the course. from past experience she knows that the results are normally distributed with a mean of 76.5% and standard deviation of 7.5%. the latest course has 2000 students and hermione offers to refund the cost of the course to any student who does not score a certain percentage.
    what should this percentage be if hermione is only prepared to refund 3 students?
    justify your answer with calculations and include at least ONE diagram in your solution.

    kk.. well ive got an answer with not much working and wonder if there is any more and i cannot find a diagram to use. can someone please help??
    Great! Don't complain about "not much working". What working did you do and what answer did you get? I think I might include a "normal curve" graph showing the values given.
    Last edited by HallsofIvy; June 21st 2009 at 04:22 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Standard Deviation in Normal Distribution is Zero!
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2011, 07:26 AM
  2. Normal Distribution - Mean and Standard Deviation
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 1st 2010, 08:50 PM
  3. normal distribution, find standard deviation
    Posted in the Statistics Forum
    Replies: 3
    Last Post: April 21st 2009, 04:12 AM
  4. Normal distribution and standard deviation?
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 7th 2009, 01:24 AM
  5. Standard Deviation and Normal Distribution
    Posted in the Statistics Forum
    Replies: 8
    Last Post: January 27th 2006, 10:48 AM

Search Tags


/mathhelpforum @mathhelpforum