S1 Question- Normal Distribution Watch

atali
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#1
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Question taken from S1 November 2004.

Question 6 part e

Normal distrubution
The mean is 34
Standard deviation= 10.7


e) Find the value of a such that P(mean - a < X < mean + a) = 0.95
How do you solve this?
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M1N1
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I think you use the Normal distribution, and you have the mean and s.d, so you can convert it into a standard normal distribution. Since you have mean in:

P(mean - a < X < mean + a) = 0.95

when you convert it to a standard normal distribution, it gets rid of the two means, but u have to divide by the standard deviation. Then read off the table for what the values would be.

I think :confused:

PK
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atali
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The mark scheme has it down as

a= 1.96 x 10.7 = 20.97....

I don't understand where the 1.96 comes from.
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Jaswarbrick
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1.96 is the z-score for the 97.5th percentile.
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atali
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Why do they use the 97.5th percentile z value?

In the question it says 0.95 so I thought you put in the 95th percentile vaule.
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stratomaster
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1-0.95=0.05
(0.05/2)=0.025
1-0.025=0.975
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atali
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Thanks alot!!:top:
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