probability...normal distribution

**sdudley24** · May 5th 2008, 08:19 AM

Assume you have a Normal Distribution with a mean of 7.5 and a standard deviation of 3.

What is the probability that X is greater than 8.5?

What is the probability that X is greater than 6.5?.

What is the probability that X is greater than 3 but less than 5.5?

What is the probability that X is less than 7.5?

**janvdl** · May 5th 2008, 11:28 AM

Excuse me if this is wrong, I only started with it today in class... But seeing as no-one else is answering I might as well take the chance and see if I can help.

Originally Posted by sdudley24

Assume you have a Normal Distribution with a mean of 7.5 and a standard deviation of 3.

What is the probability that X is greater than 8.5?

$P(X > 8,5)$

$= 1 - P(X < 8,5)$

$= 1 - P( \frac{X - 7,5}{3} < \frac{8,5 - 7,5}{3} )$

$= 1 - P(Z < \frac{1}{3})$

$= 1 - \Phi (\frac{1}{3})$

$= 1 - 0,6293$

$= 0,3707$

What is the probability that X is greater than 6.5?.

$P(X > 6,5)$

$= 1 - P(X < 6,5)$

$= 1 - P( \frac{X - 7,5}{3} < \frac{6,5 - 7,5}{3} )$

$= 1 - P(Z < - \frac{1}{3})$

$= 1 - \Phi (- \frac{1}{3})$

$= 1 - 0,3707$

$= 0,6293$

What is the probability that X is greater than 3 but less than 5.5?

$P(3 < X < 5,5)$

$= P( \frac{3 - 7,5}{3} < \frac{X - 7,5}{3} < \frac{5,5 - 7,5}{3} )$

$= P(- \frac{3}{2} < Z < - \frac{2}{3})$

$= \Phi (- \frac{2}{3}) - \Phi (- \frac{3}{2})$

$= 0,2514 - 0,0668$

$= 0,1846$