Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    1. In an old computer game a white square representing a ball appears at random at the top of the playing area, which is 24 cm wide, and moves down the screen. The continuous random variable X represents the distance, in centimetres, of the dot from the left-hand edge of the screen when it appears. The distribution of X is rectangular over the interval [4, 28].

    During a single game, a player receives 12 “balls”.
    Q: Find the probability that the ball appears within 3 cm of the middle of the top edge of the playing area more than four times in a single game.

    2. Assuming the probability of obtaining more heads than tails is 5/16 when four fair coins are flipped then..

    The four coins are flipped 5 times and more heads are obtained than tails 4 times.

    Stating your hypotheses clearly, test at the 5% level of significance whether or not there is evidence of the probability of getting more heads than tails being more than 5/16.

    --------

    1. The answer is: let y = no. within 3cm of the middle therefore X~B(12, 0.25)

    But how do you get 0.25 as your probability?

    2. The answer is 0.0358<0.05 and therefore makes the alt. hypothesis significant but I don't understand how this answer is obtained.

    Thanks so much and will plus rep in return.
    Offline

    15
    ReputationRep:
    (Original post by Apple24)
    1. In an old computer game a white square representing a ball appears at random at the top of the playing area, which is 24 cm wide, and moves down the screen. The continuous random variable X represents the distance, in centimetres, of the dot from the left-hand edge of the screen when it appears. The distribution of X is rectangular over the interval [4, 28].

    During a single game, a player receives 12 “balls”.
    Q: Find the probability that the ball appears within 3 cm of the middle of the top edge of the playing area more than four times in a single game.

    1. The answer is: let y = no. within 3cm of the middle therefore X~B(12, 0.25)

    But how do you get 0.25 as your probability?
    If X is rectangluar, how is it also binomial? If you mean Y ~ B(12, 0.25) then I'm still confused.

    Within 3cm means that you need to cut 6 cms off the 24 cm screen (3 cm from each side), which leaves just 18 cm of the screen. Now since X is rectangular, there's a 1/24 chance of it appear in any one spot. We can allow it to enter any of the 18 spots, so there's an 18/24 = 0.75 chance of it appearing in the desired area. Not sure why they say 0.25.

    I'd say Y ~ B(12, 0.75) if Y = the number of balls appearing in the 18 cm area.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Swayum)
    If X is rectangluar, how is it also binomial? If you mean Y ~ B(12, 0.25) then, I'm still confused.

    Within 3cm means that you need to cut 6 cms off the 24 cm screen (3 cm from each side), which leaves just 18 cm of the screen. Now since X is rectangular, there's a 1/24 chance of it appear in any one spot. We can allow it to enter any of the 18 spots, so there's an 18/24 = 0.75 chance of it appearing in the desired area. Not sure why they say 0.25.

    I'd say Y ~ B(12, 0.75) if Y = the number of balls appearing in the 18 cm area.
    Sorry, I did mean Y~B

    http://www.mathsandscience.org/resources/S2Fmarks.pdf

    Question 3c markscheme :confused:
    Offline

    15
    ReputationRep:
    Maybe I'm misinterpreting what it means by "within 3 cm" - it could mean that the ball must appear within a 6 cm region in the middle, in which case it'd be 6/24 = 0.25.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thanks very much for your help! I think I understand

    Anyone for question two?
 
 
 
  • 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.

  • Poll
    Would you rather give up salt or pepper?
    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
  • 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.

  • 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

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