Question

Suppose x is random variable with normal distribution (u,sigma^2) distribution and p(x<=0)=1/3 and p(x<=1)=2/3 what are the values of u and sigma? Please show me the steps to solve such a question
Thank you

Answer 1

the z-score is the number of standard deviations (σ's) that a value lies from the mean

the z-score table gives the probability of a score's position in a normal distribution

eg. the table gives the mean (z-score, zero) a probability of .5
... half of the population lies below the mean

p = 1/3 for x<=0
... from the table ... zero is .43 σ below the mean

p(x<=1)=2/3
... from the table ... 1 is .43 σ above the mean

Answer 2

Thanks for the answer but I still dont get it how did you get the 0.43?

Answer 3

http://davidmlane.com/hyperstat/z_table.html

Answer 4

click scond circle
put in area = .3333
and area = .6667
and you will get that -.43 and + .43
which means the mean is halfway between 0 and 1 :)

Answer 5

now if the distance from 0 to 1 is 2*.43 sigma, what is sigma?

Answer 6

Thanks alot I have tried coming up algebrically with 0.43 but still no luck there is formula like x-u/sigma but still cant use it any ideas?