S1 variance

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

Reply 1

Gaz031

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?