# Thread: I can't figure this out...

1. ## 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)?

2. 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 $X$, then:

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

where $\Phi(z)$ denotes the cumulative standard normal distribution, which you look up in a table.

3. 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