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AQA STATISTICS 1B Problem! (Normal Distribution)

Hi guys, this is the question

UPVC facia board is supplied in lengths labelled as 5 metres. The actual length, X metres, of a board may be modelled by a normal distribution with a mean of 5.08 and a standard deviation of 0.05

i) Determine the probability that the mean length of a random sample of 4 boards:

a) exceeds 5.05 metres

b) is exactly 5 metres.

Thankyou! any help will be massively appreciated!
Reply 1
Original post by Taylor_R
Hi guys, this is the question

UPVC facia board is supplied in lengths labelled as 5 metres. The actual length, X metres, of a board may be modelled by a normal distribution with a mean of 5.08 and a standard deviation of 0.05

i) Determine the probability that the mean length of a random sample of 4 boards:

a) exceeds 5.05 metres

b) is exactly 5 metres.

Thankyou! any help will be massively appreciated!


So you know that its a random sample of 4 boards: so n=4

new standard dev = 0.05/2= 0.025

X~N(5.08, (0.025)^2)

to find the z value of 5.05 metres:

z= 5.05-5.08/0.025 = -1.2

now draw your diagram and you want Z to exceed -1.2 (in other words be greater than -1.2)

Z>-1.2 is the same as Z<1.2 = 0.88493

For the next one exactly 5 metres is 0 because if you draw the graph and find the z value for 5 metres- if its exactly 5 there is no probability area to evaluate!
Reply 2
Original post by marek35
So you know that its a random sample of 4 boards: so n=4

new standard dev = 0.05/2= 0.025

X~N(5.08, (0.025)^2)

to find the z value of 5.05 metres:

z= 5.05-5.08/0.025 = -1.2

now draw your diagram and you want Z to exceed -1.2 (in other words be greater than -1.2)

Z>-1.2 is the same as Z<1.2 = 0.88493

For the next one exactly 5 metres is 0 because if you draw the graph and find the z value for 5 metres- if its exactly 5 there is no probability area to evaluate!


Thankyou so much, so the second part if it asks me to find anything exact it has 0 area?/probability? Thanks alot dude:smile:
Reply 3
Original post by Taylor_R
Thankyou so much, so the second part if it asks me to find anything exact it has 0 area?/probability? Thanks alot dude:smile:


yeah because nothing exists on either side!
Reply 4
Anyone done the may 2010 statistics paper?
Reply 5
Original post by qwerty54321
Anyone done the may 2010 statistics paper?


Yeah I've done most of it :smile:
Reply 6
HELP! Does anyone know how to work out the line of regression (y on x) when you only have the values for sigma x, sigma x^2, sigma y, sigma y^2 and sigma xy?? I've worked out r but I don't know how to do the regression equation from this data.
Reply 7
Original post by em_cart
HELP! Does anyone know how to work out the line of regression (y on x) when you only have the values for sigma x, sigma x^2, sigma y, sigma y^2 and sigma xy?? I've worked out r but I don't know how to do the regression equation from this data.


Don't worry, it's in the formula book that AQA give !
Reply 8
Original post by em_cart
Yeah I've done most of it :smile:


Ah I had a question but have realised my mistake now, thanks anyway. Good luck.
Reply 9
Original post by qwerty54321
Don't worry, it's in the formula book that AQA give !


Thank you :smile: Now I've worked out b but how can I work out a?? :colondollar:
gud luck everyone hope the exam is easy
Original post by em_cart
Thank you :smile: Now I've worked out b but how can I work out a?? :colondollar:


a = ybar - b(xbar)
Reply 12
Original post by qwerty54321
a = ybar - b(xbar)


Ohhhh! Thank you, I've done it now :biggrin:
Original post by marek35
So you know that its a random sample of 4 boards: so n=4

new standard dev = 0.05/2= 0.025

X~N(5.08, (0.025)^2)

to find the z value of 5.05 metres:

z= 5.05-5.08/0.025 = -1.2

now draw your diagram and you want Z to exceed -1.2 (in other words be greater than -1.2)

Z>-1.2 is the same as Z<1.2 = 0.88493

For the next one exactly 5 metres is 0 because if you draw the graph and find the z value for 5 metres- if its exactly 5 there is no probability area to evaluate!




How do you know the new standard dev? i get that N is 4 but how do you work our that st dev is 0.05/2?
Thanks in advance :biggrin:
Now i realise this topic is few years old, hahaha maybe i wont get any answers xD

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