Normal distrobution? how is it done

[almohandes]

normal distrobution? how is it done!

Problem:
suppose that the heights of men are normally ditributed with a mean of 174 cm and a standard deviation of 10cm and the heights of women are normally distrobuted with a mean of 165cm and a standard deviation of 3 cm. If a man and woman are selected independently at random, find the probability that the woman is taller than the man.

1.use a random normal generator to simulate the situation.
2.explain your simulation method clearly so that someone else can follow it.
3.Carry out at least 50 trials on spreadsheet 1.(hint: the decision command =IF(B2>A2,"Yes","No") may be useful).
4.use your trials to answer the question.

anyone know how to do this on Ms excel because i have never done it b4?and what is meant by "use a random normal generator to simulate the situation".
does anyone know some important points that should be listed in the tool and the trial?.
and what are those commands, like the one in question 3 are there more of them that I should know?.

could someone please help me?

 

[HallsofIvy]

A "random normal generator" is an algorithm that gives a list of random numbers according to the standard normal distribution rather than the uniform distribution (which is what most random number generators give). I don't know if there is such a thing in Excel. Here is a link to a page that gives an algorithm:
http://www.cast.uark.edu/~kkvamme/ACN37.htm
(From the "Archeological Computing newsletter"!)

 

[tacman]

The normal distribution, also known as the Gaussian distribution, is a probability distribution that is commonly used in statistics to model continuous random variables. It is a bell-shaped curve that is symmetric around the mean, with most of the data falling within one standard deviation of the mean. The mean and standard deviation are important parameters in the normal distribution, as they determine the shape and location of the curve.

To simulate the situation described in the problem, we can use a random normal generator. This is a function that generates random numbers that follow a normal distribution with specified mean and standard deviation. In Microsoft Excel, this function is called "NORM.INV" and can be found under the "Formulas" tab. To use it, we need to provide the mean and standard deviation as inputs, and it will generate a random number that follows the normal distribution.

To simulate the situation of selecting a man and woman at random, we can create two columns in a spreadsheet - one for the heights of men and one for the heights of women. In each column, we can use the "NORM.INV" function to generate 50 random numbers that follow the given mean and standard deviation. We can then use the "IF" function to compare the heights of the man and woman in each trial and determine if the woman is taller than the man.

The "IF" function is a logical function in Excel that allows us to specify a condition and return a value if the condition is true, and a different value if the condition is false. In this case, we can use the condition "if the height of the woman is greater than the height of the man" and return a value of "Yes" if the condition is true, and "No" if the condition is false. This will help us to keep track of how many times the woman is taller than the man in our 50 trials.

Some important points that should be listed in the tool and the trial are:
- The mean and standard deviation for the heights of men and women.
- The number of trials (50 in this case).
- The generated heights for each man and woman in each trial.
- The result of the "IF" function, indicating whether the woman is taller than the man in each trial.
- The overall probability of the woman being taller than the man, calculated by dividing the number of "Yes" results by the total number of trials.

In summary, to simulate the given situation and find the probability