1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Normal and binomial distribution: using Z-scores to find answer

  1. Jun 10, 2013 #1
    The prices for bananes that a fruit shop would have to pay to keep them in stock have a mean of $1.35/kg and a standard deviation of 18 cents. The owner will not pay more than a certain price, but manages to keep stock 8% of the time. What is the maximum price the ownwer will pay?

    I found 0.08 on a Z-score table and it was approximately Z=0.201. This is a negative number because it is less than the mean (or so i figured). I used the formula Z=(X-μ)/σ and re-arranged to get (-0.201*0.18)+1.35= price he is willing to pay. This then gave $1.31.
  2. jcsd
  3. Jun 11, 2013 #2


    User Avatar
    Homework Helper

    "...but manages to keep stock 8% of the time"

    means the probability the owner will have stock left at the end of the day is 8%, or 0.08. Stated another way, there is only an 8% chance that the demand for his product will be greater than what he has on hand. This means the Z-score you seek is the one that cuts off the right-hand 8% of the distribution, so should not be a negative value. Your basic idea for attacking the problem seems correct, except for this item.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted