normal distribution question . . . please help (s1)

i no this is probably simple, but i can't seem to b able to do this normal distribution question . . . .

The random variable X has a normal distribution with mean 16 and variance 0.64. Find x, such that P(X=x) = 0.025
:confused:

can someone please help me

Reply 1

username22878

Are you sure it says 'X=x' and not X<x or X>x, as far as I remember you couldnt get equalities using the normal distribution.

Reply 2

amirvj

woops. sowi typin error . . . its ment 2 b P(X < x) not P(X=x). hehehe!!

Reply 3

Jonny W

Statistical tables say that Phi(1.960) = 0.975. [Phi is the Greek letter $\Phi$ .]

So there is probability 0.025 that a normal random variable is more than 1.960 standard deviations below its mean. [There is also probability 0.025 that a normal random variable is more than 1.960 standard deviations above its mean. But we don't need that for this question.]

So x = mean - 1.960*sd = 16 - 1.960*0.8 = 14.432.

Reply 4

cherc2005

X~N (16 , 0.64)

P(X < x) = 0.025

An alternative to this is by looking at the percentage tables, it tells us that when p = 0.025, z = 1.9600. Since we are looking at the left of the normal distribution, the z value is negative (see attached image).

Therefore:

P(X < x)

= P(Z< x – 16 / √0.64 ) = -1.96

x – 16 = -1.96 * √0.64

x = -1.568 + 16

x = 14.432

NORMAL.JPG6.3KB