URGENT help please ! S1

please can someone guide me through how to do this? I have no idea
Any help will be much apprecaited. Thanks in advance to anyone does help !

Question:
the lifetime of an electrical component may be modelled by a normal distribution, X, which means 2500 hours and variance 900 hours 2. Find the value of P(X>a)=0.8

Ive started off kinda :/
Mean= 2500
Variance = 900^2

X~N(2500 , 900^2)
P(X > a) = 0.8
??

x

Variance is 900 not 900²

Variance is 900 not 900²

If you don't mind would you be able to assist me on what do next?
I'm assuming that I should look at the table of normal distribution functions and look for the value of 0.8 ??

page 23 onwards
http://madasmaths.com/archive/maths_booklets/statistics/normal_distribution_calculations.pdf

Hey thanks

I alway get confused on this bit:

You see in the attachment how does the 0.95 become -1.645??

Hey thanks

I alway get confused on this bit:

You see in the attachment how does the 0.95 become -1.645??

look at the normal tables backwards

you are inverting probability of 0.95

(the minus is because the "cut" is on the left of the mean)

You do 1-0.95 which is 0.05. The z value for 0.05 is 1.6449. Because what you're looking for is on the left hand side, the value is negative.

Guys can you check this :/
Thanks for your help!

the is no INVERSE PHI of 0.2 in standard tables

you only do 1 minus if you are inverting probabilities under 0.5

however this self corrects since INVERSE PHI of 0.8 is indeed 0.8416

the issue is that this is minus if you draw a picture since the "cut" is on the left.

the is no INVERSE PHI of 0.2 in standard tables

you only do 1 minus if you are inverting probabilities under 0.5

however this self corrects since INVERSE PHI of 0.8 is indeed 0.8416

the issue is that this is minus if you draw a picture since the "cut" is on the left.

Oh sorry.
Thanks so much
So the final answer is correct then ?

No because you need -0.8416

the "cut" is on the left

you do not do NORMAL without a diagram....

the mean is 2500 hours, the standard deviation is 30 hours. you need to look up the z value for 0.8... this will be about 0.84

0.84 = (2500 - a)/30

rearrange to find a.

we put 2500 - a instead of a - 2500 because the value of a must lie to the left of the mean.

But that gives the same answer :/
I accidentally forgot to put it in the attachment when I wrote it

So the answer is -2525 ?

0.84*30 = 2500 - a

so a should be a positive number ?