• A question about a normal distribution problem

I found this on your website and I was just wondering what the answer was because I don't really know how to do it :-
"A geneticist working for a seed company develops a new carrot for growing in heavy clay soil. After measuring 5000 of these carrots it can be said that carrot length X is normally distributed with mean µ = 11.2cm and s = 1.1cm.

(i) What is the probability that X will take on a value in the interval 10.0 <= X <= 13.0?"

• This is widely used in statistics specially where the distribution of variable is not following a fixed algebraic formula trend - that means the values of variable are totally random.

In this case also we do not know what will be the length of a carrot - it is random.

The random variable X ( length of carrot) is having a normal distribution with mean mu (µ) and standard deviation sigma (s ) and its probability distribution function is given by -
f(X) = a math formula containing X, mu and sigma.

Now if you want to calculate probability between two values X1 and X2 then the area of normal distribution curve between these two points is the answer.

Mathematically it is found by integrating f(X) from X1 to X2.

With the above background material you can try to solve the numerical problem by integrating yourself.

If you have any problem either consult a basic text book on statistics or go to following interactive math site in net -
www.intmath.com

Knowledge is power.

• Let x1=10.0 , x2= 13.0,
We get two points Z1 and Z2 by substituting: Z= (x-u)/(s/n).
Using the formula we get, Z1= -1.09.
Z2= 1.63.
Using a Z curve you now can determine the probability of X.

The stronger a light shines the darker are the shadows around it.