Hey there! Sign in to join this conversationNew here? Join for free

Statistics Watch

Announcements
    • Thread Starter
    Offline

    0
    ReputationRep:
    Times can be modelled by X~N(65,20)

    Given that the times are independent from each day, determine that in a period of 6 days;

    the time to complete each crossword is less than 60 minutes

    her mean completion time is less than 60 minutes

    completely forgotten how to do these, so any help appreciated.
    • Thread Starter
    Offline

    0
    ReputationRep:
    anybody?
    • Offline

      14
      (Original post by Oti93)
      Times can be modelled by X~N(65,20)

      Given that the times are independent from each day, determine that in a period of 6 days;

      (1) the time to complete each crossword is less than 60 minutes

      (2) her mean completion time is less than 60 minutes

      completely forgotten how to do these, so any help appreciated.
      I assume that "she" does one crossword each day, and these questions want you to determine the probability of these outcomes.

      The distribution tells you that she completes these crosswords with a mean time of 65 minutes and a variance of 20 minutes.

      Over 6 days, she does 6 crosswords i.e. you are taking a random sample of 6 from this distribution.

      Problem (1)
      I think this is the probability of getting 6 times that are all less than 60 minutes. The probability of getting 1 time that is less than 60 minutes is given by the distribution as:

      P_{t<60} = P(t < 60), where P(t < 60) is given by the cumulative normal distribution function, or can be looked up in normal distribution tables after converting to the standard distribution, commonly written as Z.

      Since we are now looking at a problem with a fixed probability, p = P_{t<60} and a discrete number of trials, n = 6, it becomes one of a binomial distribution, where the general binomial distribution is:
      P = B(n,p).

      However, since the problem only asks for the probabiliity where all trials are successful (i.e. all crosswords are completed in under 60mins), the calculation is simple, it is just:

      P_{(1)} = p^n


      Problem (2)
      Use the Central Limit Theorem. The probability distribution of a random sample has the same mean as the population, but its variance is modified. Find out how, and this gives you a new distribution from which you can calculate P'(t<60).
     
     
     
  1. See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  2. Poll
    Will you be richer or poorer than your parents?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  3. See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  4. The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.