# Normal Distribution

• Apr 22nd 2006, 07:05 PM
darren_a1
Normal Distribution
Hope some one can help me with this

Quote:

Let X1,X2 .... X16 be a random sample from a normal distribution N(77,25).

Compute a)P(77<X<79.5)
b) P(74.2<X<78.4)
Cheers ;)
• Apr 23rd 2006, 12:26 AM
CaptainBlack
Quote:

Let X1,X2 .... X16 be a random sample from a normal distribution N(77,25).

Compute a)P(77<X<79.5)
b) P(74.2<X<78.4)
What is X? the sample mean?

RonL
• Apr 23rd 2006, 06:24 AM
darren_a1
Yes -- it's actually X with a little line over the top- i didnt know how to put it in here.

Cheers
• Apr 23rd 2006, 08:13 AM
CaptainBlack
Quote:

Let X1,X2 .... X16 be a random sample from a normal distribution N(77,25).

Compute a)P(77<X<79.5)
b) P(74.2<X<78.4)
The sample mean of a sample of size $n$ from a normal distribution
$N(\mu,\sigma^2)$ has a normal distribution; $N(\mu,\sigma^2/n)$.

So in this case the SD of the sample mean is $5/4$ so:

$
P(77
$P(\bar X$,

Which may be looked up in a suitable table:

$
P(77$
.

The second question is:

$
P(74.2
$P(\bar X-2.24 \sigma $

Which from tables I make $0.8686-0.0125=0.8561$

RonL