# A Level Normal Distribution question

• Mar 20th 2007, 02:48 PM
jonannekeke
A Level Normal Distribution question
Hi, I've been looking at this question for nearly an hournow and I can't figure out what to do, I've looked through my notes and my textbook and nothing helps so could someone please talk me through what I need to do?

Question:
1. An athlete believes that her times for running 200 metres in races are normally distributed
with a mean of 22.8 seconds.
(a) Given that her time is over 23.3 seconds in 20% of her races, calculate the variance of
her times.
[5 marks]
(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?
[3 marks]

• Mar 20th 2007, 03:00 PM
CaptainBlack

RonL
• Mar 20th 2007, 03:03 PM
jonannekeke
Thanks

Where do you get the 0.84 from?
• Mar 20th 2007, 03:19 PM
CaptainBlack
Quote:

Originally Posted by jonannekeke
Thanks

Where do you get the 0.84 from?

Table look-up in the table of the cumulative standard normal distribution.

For the standard normal P(z<0.84)~=0.8, so P(z>0.84) ~= 0.2

RonL
• Mar 20th 2007, 03:43 PM
jonannekeke
I know I sound really stupid but I sill don't understand :(

Oooo never mind, I just found the answer to this question in my book, we did this question ages ago as practice but thanks for your help anyway :)