Turn on thread page Beta

s2 watch

Announcements
    • Thread Starter
    Offline

    2
    ReputationRep:
    eggs are sold in boxes of 12. for each egg the probability that it is cracked is 0.05 independently of all other eggs. a randon sample of n boxes is selescted and the variance of the sample mean is 0.019 find the value of n??????????????????????????????? ??????????????????


    thanks
    Offline

    8
    ReputationRep:
    We need the formula Var(aZ + b) = a^2 Var(Z), which works for any random variable Z and any numbers a and b.

    --

    Let X be the number of broken eggs in the sample.

    X ~ Bin(12n, 0.05)
    Var(X) = 12n*0.05*0.95 = 0.57n

    Let Y = X/n be the number of broken eggs per box in the sample.

    Var(Y) = Var(X)/n^2 = 0.57/n

    [Var(Y) goes down as n increases.]

    The question says that Var(Y) = 0.019. So n = 0.57/0.019 = 30.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Jonny W)
    We need the formula Var(aZ + b) = a^2 Var(Z), which works for any random variable Z and any numbers a and b.

    --

    Let X be the number of broken eggs in the sample.

    X ~ Bin(12n, 0.05)
    Var(X) = 12n*0.05*0.95 = 0.57n

    Let Y = X/n be the number of broken eggs per box in the sample.

    Var(Y) = Var(X)/n^2 = 0.57/n

    [Var(Y) goes down as n increases.]

    The question says that Var(Y) = 0.019. So n = 0.57/0.019 = 30.

    im doin ocr s2 and ive never come across the formula
    Var(aZ + b) = a^2 Var(Z), is it from s1 and i cant remember it or is there a different way?
    Offline

    8
    ReputationRep:
    Sorry, the formula comes from OCR S3 (it's in Edexcel S1).

    You are meant to know however that

    Var(sample mean) = sigma^2 / n

    where sigma^2 is the variance of the distribution and n is the sample size.

    In our case, sigma^2 = variance of number of broken eggs in a box = 12*0.05*0.95 = 0.57. So Var(sample mean) = 0.57/n.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Jonny W)
    Sorry, the formula comes from OCR S3 (it's in Edexcel S1).

    You are meant to know however that

    Var(sample mean) = sigma^2 / n

    where sigma^2 is the variance of the distribution and n is the sample size.

    In our case, sigma^2 = variance of number of broken eggs in a box = 12*0.05*0.95 = 0.57. So Var(sample mean) = 0.57/n.
    thankyou i get it now!
 
 
 
Turn on thread page Beta
Updated: January 3, 2005

University open days

  • Brunel University London
    Postgraduate Open Evening Postgraduate
    Wed, 23 Jan '19
  • University of the West of England, Bristol
    Undergraduate Open Afternoon - Frenchay Campus Undergraduate
    Wed, 23 Jan '19
  • University of East London
    Postgraduate Open Evening Postgraduate
    Wed, 23 Jan '19
Poll
Are you chained to your phone?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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

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.