Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By romsek

Thread: Probabilities and Normal Distribution Question

  1. #1
    Newbie
    Joined
    Oct 2018
    From
    Canada
    Posts
    2

    Probabilities and Normal Distribution Question

    I can't seem to find the answer for this question; so far I've tried weighted averages and finding the closest equivalent z-score for the percentages, but I'm at a loss.

    The heights of individuals in a mall are normally distributed. If 66% of the shoppers are shorter than 160 cm and 82% of the shoppers are shorter than 170 cm, determine the mean height of the shoppers. Round your answer to the nearest hundredth of a centimeter if necessary.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,501
    Thanks
    2846

    Re: Probabilities and Normal Distribution Question

    There are two parameters to solve for and you've got two conditions.

    Let $\Phi(x)$ be the CDF of the standard normal distribution

    $\Phi\left(\dfrac{160-\mu}{\sigma}\right) = 0.66$

    $\Phi\left(\dfrac{170-\mu}{\sigma}\right) = 0.82$


    $\dfrac{160-\mu}{\sigma} = \Phi^{-1}(0.66) = 0.412463$

    $\dfrac{170-\mu}{\sigma} = \Phi^{-1}(0.82) = 0.915365$

    It's a simple algebra problem now which I leave for you to solve.
    Thanks from HallsofIvy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Jul 29th 2013, 10:19 AM
  2. another Normal Distribution question
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Aug 31st 2011, 09:50 PM
  3. Question on normal distribution
    Posted in the Statistics Forum
    Replies: 4
    Last Post: Sep 14th 2010, 11:39 PM
  4. Normal Distribution Question Help!?
    Posted in the Statistics Forum
    Replies: 0
    Last Post: Feb 20th 2010, 04:04 PM
  5. Normal distribution question.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Oct 23rd 2009, 06:52 PM

/mathhelpforum @mathhelpforum