normal distribution

[jimjohn]

ok so i know that ifi have a sample mean, and i take 1.96 standard deviations above and below this mean, this gives me a 95 % confidence interval for the mean. and that if i did the same thing with 1.645 standard deviations, it would give me a 90% confidence interval.

for people who use value at risk, the common thing is to take 1.645 standard deviations below the mean = x, and then we can conclude we're 95 % confident the mean is not going to be below x.

can someone plz explain how we get the second paragraph from the first paragraph. i completely understand how the first works, but i just dont know how to use this info to conclude the second. thx.

[Hector Maletta]

The area below -1.645 SD comprises 5% of the total area under the normal
curve (and the area above +1.645 SD also comprises 5%, hence the area in
between is 90%). The area above -1.645 SD comprises therefore 95% of the
total area under the curve. So if you are interested only in not being below
the mean, taking -1.645 ensures that you are not below the mean in 95% of
the cases.
Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
jimjohn
Sent: 06 March 2008 17:16
To: [hidden email]
Subject: normal distribution

ok so i know that ifi have a sample mean, and i take 1.96 standard
deviations
above and below this mean, this gives me a 95 % confidence interval for the
mean. and that if i did the same thing with 1.645 standard deviations, it
would give me a 90% confidence interval.

for people who use value at risk, the common thing is to take 1.645 standard
deviations below the mean = x, and then we can conclude we're 95 % confident
the mean is not going to be below x.

can someone plz explain how we get the second paragraph from the first
paragraph. i completely understand how the first works, but i just dont know
how to use this info to conclude the second. thx.
--
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