normal distribution

[Jellekool]

Hi everyone!

I have a question about the answer of question 19a and e. question a: Find the probability that X is greater than 60. Why do they do 0,5 -0,3944 and not 1 - ...?
Question e was: the probability is 0,05 that X is in the symmetric interval about the mean between which two numbers? additional info: mean is 50 and sigma squared is 64. I don't really understand what I have to do here. Can anyone help me out?

Thanks in advance!

 

[Dason]

I'm guessing the z-table they use gives the area between 0 and whatever value you want. So if it asked for find P(0 < Z < some_value) then when you look up some_value in the table it will give you that probability directly. There are many different ways these tables get made so you just need to make sure you know what the particular table you're using actually does.

For your second question they're asking what two values are such that 1) they are symetric around the mean (so they have the same distance from the mean) and 2) the probability of being between those two values is .05. So essentially they asking you to solve for 'a' and 'b' in P(a < X < b) = 0.05 where a and b the same distance from the mean. Another way to put that is to solve for c in the following P(50 - c < X < 50 + c) = 0.05

 

[Jellekool]

thank you very much, but I still don't really understand the second question..

Can someone write it out step by step?

 

[obh]

symmetric around the 0.5, so half probability to the right and half probability to the left, the total is 0.05

p(z<=Z1) - p(z<=Z2)=0.05

0.5+(0.05/2)=0.525
0.5-(0.05/2)=0.475

p(z<=Z1)=0.525 => Z1 = 0.0627061 => (x1-50)/8=~0.06 => x1=50.48
p(z<=Z2)=0.475 => Z2 = -0.0627061 => (x2-50)/8=~0.06 =>x2=49.52

Inv Z(0.525)= 0.0627061 =>
Inv Z(0.475)= 0.0627061 =>

P( x ≤ 50.501649 ) = 0.525
P( x ≤ 49.498351 ) = 0.475