I can't figure this out...

• Oct 29th 2008, 01:07 PM
greenpumpkins
I can't figure this out...
Assume the random variable X is normally distrubted with mean = 50 and standard deviation = 7. Compute its probability.

P(34 < X < 61)?
• Oct 29th 2008, 02:48 PM
CaptainBlack
Quote:

Originally Posted by greenpumpkins
Assume the random variable X is normally distrubted with mean = 50 and standard deviation = 7. Compute its probability.

P(34 < X < 61)?

Compute the z-scores for the endpoints of the interval for \$\displaystyle X\$, then:

\$\displaystyle
P(34< X< 61)=P(-16/7<Z<11/7)=P(Z<11/7)-P(Z<-16/7)\$ \$\displaystyle =\Phi(11/7)-\Phi(-16/7)
\$

where \$\displaystyle \Phi(z)\$ denotes the cumulative standard normal distribution, which you look up in a table.
• Oct 29th 2008, 03:39 PM
djmccabie
P(34 < X < 61) =

P( X = 61) - P( X = 34)

Using the formula Z = (X - Mean)/Std Deviation

(61 - 50)/ 7 = 1.57

(34 - 50)/7 = -2.28

ɸ(1.57) - ɸ(-2.28)

ɸ(-2.28) = 1-ɸ(2.28)

As CB mentioned ɸ basically means look it up from a standard normal distribution table

Hope this helps :)