S1 Normal Distribution Question Watch

The Polar Dude
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I'm pretty sure this topic is in the bad book in some of the A level Maths students because the questions can be sooooo random. (well for me at least )

anyways, im struggling to do this question, so I was wondering if you guys could help me

I got 0.6915 but thats wrong (but since there are 3 bicycles, i was going to multiply by 3 but thats still wrong), the answer is actually ?0.3307

The time taken in minutes, T, for a mechanic to service a bicycle follows a normal distribution with a mean of 25 minutes and a variance of 16 minutes
One afternoon the mechanic has 3 bicycles to service.
(c) Find the probability that he will take less than 23 minutes on each of the three bicycles.
(4 marks)

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thegodofgod
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(Original post by The Polar Dude)
I'm pretty sure this topic is in the bad book in some of the A level Maths students because the questions can be sooooo random. (well for me at least )

anyways, im struggling to do this question, so I was wondering if you guys could help me

I got 0.6915 but thats wrong (but since there are 3 bicycles, i was going to multiply by 3 but thats still wrong), the answer is actually ?0.3307

The time taken in minutes, T, for a mechanic to service a bicycle follows a normal distribution with a mean of 25 minutes and a variance of 16 minutes
One afternoon the mechanic has 3 bicycles to service.
(c) Find the probability that he will take less than 23 minutes on each of the three bicycles.
(4 marks)

Have you drawn a diagram / mapped the standard dev / mean onto the standard normal distribution curve?
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The Polar Dude
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(Original post by thegodofgod)
Have you drawn a diagram / mapped the standard dev / mean onto the standard normal distribution curve?
yeah, the mean is 25 and the S.D is 4 and i even did 1 minus as it asked for LESS than 23mins
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thegodofgod
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(Original post by The Polar Dude)
yeah, the mean is 25 and the S.D is 4 and i even did 1 minus as it asked for LESS than 23mins
No no - convert it using z = \frac{x - mean}{standard deviation}, so it maps onto X ~ N (0, 12)
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baffled_mathman
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(Original post by The Polar Dude)
yeah, the mean is 25 and the S.D is 4 and i even did 1 minus as it asked for LESS than 23mins
Why did you do that? You're not using an approximation requiring a continuity correction are you?
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stayd001
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Have you worked out the standard error? or used the standard deviation?
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The Polar Dude
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(Original post by baffled_mathman)
Why did you do that? You're not using an approximation requiring a continuity correction are you?
:confused: OH IM confused
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The Polar Dude
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(Original post by thegodofgod)
No no - convert it using z = \frac{x - mean}{standard deviation}, so it maps onto X ~ N (0, 12)
ok so it would be:

23-25/4 which gave me -0.5, then what?
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baffled_mathman
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(Original post by The Polar Dude)
:confused: OH IM confused
Right, let's deal with this. You know that the mean is 25 and the Standard Deviation is 4 (square root of 16). So you need to find P(Z< (23-25)/4). What do you get for that?
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The Polar Dude
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(Original post by baffled_mathman)
Right, let's deal with this. You know that the mean is 25 and the Standard Deviation is 4 (square root of 16). So you need to find P(Z< (23-25)/4). What do you get for that?
-0.5
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baffled_mathman
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(Original post by The Polar Dude)
-0.5
Yes, it's -0.5

But what's P(Z<-0.5)? That's the probability of Z being less than -0.5 on the standardised normal distribution.
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The Polar Dude
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(Original post by baffled_mathman)
Yes, it's -0.5

But what's P(Z<-0.5)? That's the probability of Z being less than -0.5 on the standardised normal distribution.
um.... im not sure but my teacher says to do symmetry, so i put -0.5 on the right of the curve and then i was told to look up the value

so i would look up 0.5 which is 0.6915 and then do 1 take away 0.6915 or am i wrong?
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The Polar Dude
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(Original post by stayd001)
Have you worked out the standard error? or used the standard deviation?
IM using the S.D which is 4
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baffled_mathman
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That's correct. So 1-0.6915 is 0.3085. This is the probability that he takes less than 23 minutes for 1 bike. Now what?
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ilovedubstep
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(Original post by thegodofgod)
No no - convert it using z = \frac{x - mean}{standard deviation}, so it maps onto X ~ N (0, 12)
Is it not standarddeviation/ the root of n?
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The Polar Dude
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(Original post by baffled_mathman)
That's correct. So 1-0.6915 is 0.3085. This is the probability that he takes less than 23 minutes for 1 bike. Now what?
this is where im confused
i thought times by 3 but im not too sure
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baffled_mathman
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(Original post by ilovedubstep)
Is it not standarddeviation/ the root of n?
No, it isn't.
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ilovedubstep
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(Original post by baffled_mathman)
No, it isn't.
why..
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baffled_mathman
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(Original post by The Polar Dude)
this is where im confused
i thought times by 3 but im not too sure
Well, it should be (0.3085)^3 which is 0.0294 (4 dp). So either your book or I am wrong...
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baffled_mathman
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(Original post by ilovedubstep)
why..
I'm not writing out 3 pages to show why...it just isn't.

Look it up on Wikipedia or your statistics book.
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