Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By romsek

Math Help - Find the least value of n

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    Unknown
    Posts
    73
    Thanks
    2

    Find the least value of n

    The question goes like this:

    On average, out of every 1000 items made by a certain factory worker, 1 item is defective. The items are inspected in batches. A large number of batches, each of n items, made by the worker are inspected.. The probability of at least one defective item in a batch of n items is greater than 0.02. Find the least value of n.

    I'm not sure how to begin. Is the no. of trails n or 1000 items?

    Thank you! please add explanations too if possible!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,672
    Thanks
    1074

    Re: Find the least value of n

    Quote Originally Posted by pumbaa213 View Post
    The question goes like this:

    On average, out of every 1000 items made by a certain factory worker, 1 item is defective. The items are inspected in batches. A large number of batches, each of n items, made by the worker are inspected.. The probability of at least one defective item in a batch of n items is greater than 0.02. Find the least value of n.

    I'm not sure how to begin. Is the no. of trails n or 1000 items?

    Thank you! please add explanations too if possible!
    the probability of that worker making a defective item is p=1/1000

    The probability of finding at least 1 defective item out of a batch N is

    1 - (1-p)^N > 0.02

    (1-p)^N < 0.98

    N\log(1-0.001) < \log(0.98) ; note the inequality flips because the log is negative

    N = \frac{\log(0.98)}{\log(0.999)} > 20.19 \Rightarrow N>21
    Thanks from pumbaa213
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2013
    From
    Unknown
    Posts
    73
    Thanks
    2

    Re: Find the least value of n

    haha (once again)thanks romsek! You've been a great help to me and my homework!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: November 26th 2012, 01:50 PM
  2. Replies: 8
    Last Post: March 22nd 2011, 04:57 PM
  3. Replies: 2
    Last Post: July 5th 2010, 08:48 PM
  4. Replies: 1
    Last Post: February 17th 2010, 03:58 PM
  5. Replies: 0
    Last Post: June 16th 2009, 12:43 PM

/mathhelpforum @mathhelpforum