Turn on thread page Beta
 You are Here: Home >< Maths

# S1 variance watch

Announcements
1. 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
2. (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).

Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 22, 2005
Today on TSR

Choose Respect

### University open days

• Manchester Metropolitan University
Wed, 14 Nov '18
• University of Chester
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
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

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