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S1 - Normal Distribution question

Hi guys, year 12 normal distribution question I'm completely baffled on how to start...

I'll type it out - i find it really hard to get it from a paragraph to a P ( X > a ) = b form...

'The distance a particular car is able to travel on a full tank of fuel can be modelled by a normal random variable D with mean 640km and standard deviation 13.5km.

A driver sets off in the car with a full tank of fuel on a journey of d km.

Find, to the nearest km, the value of d such that there is no more than a 5% chance that the car runs out of fuel.'

So far i've got the basic D ~ N (640 , 13.5^2)

but am not sure how to continue

Any help would be appreciated.
Reply 1
Avatar for Gcayte
Gcayte
14
erm, I was doing this type of question today!
have you done confidence intervals? I believe this is what this is getting at!
Well if you want no more that 5% chance the car runs out of fuel, thats 95% confidence, which is 1.96 standard deviations from the mean (basically look 0.975 in the tables gives you 1.96)
Then you work out the standard error - standard deviation/number of trial^2
Then add this value to the mean, and take this value to the mean.
Gives you the confidence intervals.
Im not really sure how to work the actual value for d, but hope the above helps a bit :smile:

On seconds thoughts I think maybe 'd' is the highest value, the one where you add the standard error*1.96 to the mean :smile:
(edited 12 years ago)
Reply 2
Avatar for lubus
lubus
12
(640-x)/13.5 = (whatever you got from the tables, i cba to check the guy above me's logic, so this may or may not be 1.96)

solve for x

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