Help!!with S1 Normal Distribution Question!

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)

i have no idea how to do this.Please if someone could go through it step by step that would be great!thanks

Reply 1

blue_n_white

mmmmmmmmmmmmm :s-smilie:

il have a look. what board are you on?

Reply 2

The West Wing

18

bekky92

X ~ N(22.8, σ^2)

P(X > 23.3) = 0.2

P(z > (23.3 - 22.8)/&#963 :wink:

= 0.2

P(z > 0.5/&#963 :wink:

= 0.2

Using the probablilty tables in the [Edexcel] formula booklet,

0.5/σ = 0.8416
σ = 0.5/0.8416
σ = 0.59411

σ^2 = 0.35296
σ^2 = 0.353 to 3sf

^^^^
Is correct

Reply 3

itsme!!

OP

4

Ok i understand upto this part: P(z > 0.5/&#963 :wink:

= 0.2
BUT you say that ' Using the probablilty tables in the [Edexcel] formula booklet,

0.5/σ = 0.8416 '

i don't see how you got that.What do you look up?because on the formula sheet there is NO 0.8416, the closest is 0.8413, with a z value of 1.00.Please help,im so confused!

Reply 4

The West Wing

18

itsme!!

Ok i understand upto this part: P(z > 0.5/&#963 :wink:

= 0.2
BUT you say that ' Using the probablilty tables in the [Edexcel] formula booklet,

0.5/σ = 0.8416 '

i don't see how you got that.What do you look up?because on the formula sheet there is NO 0.8416, the closest is 0.8413, with a z value of 1.00.Please help,im so confused!