Turn on thread page Beta

S1 variance watch

Announcements
    • Thread Starter
    Offline

    1
    ReputationRep:
    hi, can anyone help me with this:

    An athlete believes that her times for running 200 metres in races are normally distributed with a mean of 22.8 seconds.

    a) given her time is over 23.3 seconds in 20% of her races, calculate the variance of her times.

    b) the record over this distance for women at her club is 21.82 seconds. according to her model, what is the chance that she will beat this record in her next race?

    thanks
    Offline

    15
    ReputationRep:
    (Original post by mathsguru)
    hi, can anyone help me with this:

    An athlete believes that her times for running 200 metres in races are normally distributed with a mean of 22.8 seconds.

    a) given her time is over 23.3 seconds in 20% of her races, calculate the variance of her times.
    Let the variance be s² and let T be the random variable corresponding to her times.
    We know that P(T>23.3)=0.2 on the normal distribution with mean 22.8 and variance s².
    Hence, standardizing, P(z>(23.3-22.8)/(s))=0.2
    Use the tables to find (23.3-22.8)/s and hence solve for s. Hence you can square to find s², the variance.

    b) the record over this distance for women at her club is 21.82 seconds. according to her model, what is the chance that she will beat this record in her next race?
    You need to find P(T<21.82).
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 22, 2005

University open days

  • Manchester Metropolitan University
    Postgraduate Open Day Postgraduate
    Wed, 14 Nov '18
  • University of Chester
    Chester campuses Undergraduate
    Wed, 14 Nov '18
  • Anglia Ruskin University
    Ambitious, driven, developing your career & employability? Aspiring in your field, up-skilling after a career break? Then our Postgrad Open Evening is for you. Postgraduate
    Wed, 14 Nov '18
Poll
Should Banksy be put in prison?
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.