Question 1038990: Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of 4% and a standard deviation of 6%. Find the probability that the one-year return of this stock will be positive.
.
I put the figures into a formula and get this:
z(0)=(0-4)/6 = -.06667
= p(x>0) = p(z>--.06667)
= normalcdf (-0.6667, 100)
.
Unfortunately, I don't have a scientific calculator handy that will use the function normalcdf. How do I determine the rest of the equation without one? (Hoping that is possible.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can use an online statistical calculator that will do the calculations for you.
the one at the following link will spoil you because it's so easy to use and so intuitive.
http://davidmlane.com/hyperstat/z_table.html
it told me that the area under the distribution curve to the right of a z-score of -.66667 was equal to .7475.
you could also use the z-score table to find the area to the left of the indicated z-score.
it will get you in the ball park which is good enough in most cases.
the table that i used is here.
http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
this table tells me that a z-score of -.67 has .2514 of the area under the distribution curve to the left of it.
it also tells me that a z-score of -.66 has .2546 of the area under the distribution curve to the left of it.
by interpolation, i calculated that a z-score of -.667 would have approximately .25243 of the area under the distribution curve to the left of it.
this means that 1 - .25243 = .74757 of the area under the distribution curve would be to the right of it.
the online calculator is much easier to use, but you should learn how to use the table as well, even though it's unnecessary except in circumstances where you are forced to use it rather than the calculator.
if you had the TI-84 plus, you would do the following:
you would go to distr and you would select normalcdf.
you would enter (-2/3,99999) and it would tell you that the area under the distribution curve is equal to .747507533.
probably 5 nines would give you sufficient accuracy.
in fact, entering (-2/3,100) was sufficient to get you the same answer as well.
|
|
|
