# normal distribution

• Jun 1st 2007, 05:10 AM
m777
normal distribution
Hello,
plz try to solve this question.
Thanks.
Question:
Given a normal distribution with μ=40 and σ = 6 , find
(a) the area below 32
(b) the area above 27
(c) the area between 42 and 51
(d) the x value that has 45% of the area below it
(e) the x value that has 13% of the area above it
• Jun 1st 2007, 06:15 AM
ThePerfectHacker
Quote:

Originally Posted by m777
Given a normal distribution with μ=40 and σ = 6 , find
(a) the area below 32

Find the z-score,
$\displaystyle \frac{40-32}{6} = z \to z =1.33$
The corresponding value is .408 on the table.
Thus, $\displaystyle P(32 \leq x \leq 40) = .408$.
But then,
$\displaystyle P(x\leq 32) + P(32\leq x \leq 40) = .5$
Thus,
$\displaystyle P(x\leq 32) = .092$
Quote:

(b) the area above 27
Find the corresponding z-score:
$\displaystyle \frac{40-27}{6}\approx 2.166$
The corresponding value is .484
Thus,
$\displaystyle P(27\leq x\leq 40) = .484$
But then,
$\displaystyle P(27\leq x) = P(27\leq x \leq 40)+P(40\leq x) = .484+.5 = .984$