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I am performing a study on individuals heights, comparing 4 different areas of my city. I want to calculate the probability of each of the 4 Areas being the tallest:

• Example: What is the probability of A1 being the tallest Area ?

All of the 4 areas have a normal distribution on their heights

Areas = A1, A2, A3, A4

 

A1 = Mean 180 with SD 7.2
A2 = Mean 178 with SD 7
A3 = Mean 176 with SD 9
A4 = Mean 182 with SD 8.4

I don't know now, how to go forward from here. I do know how to compare two Areas I saw an example here:

For example, if I wanted to know the probability of A1 being taller than A2, I would get the Normal distribution of the difference of $A1-A2$, like:

$$D = A1 - A2 = 180 - 178 = 2\quad\text{ ----- this for the mean}$$

And for the SD, I get $(7.2^2 + 7^2)^{0.5} = 10.041$

So using the distribution D with mean 2 and SD 10.041, I just calculate the cumulative distribution for D>0. But, how to do the same analysis for the 4 areas?

$$A1 > (A2\ \&\ A3\ \&\ A4)$$

Thank you.

I am performing a study on individuals heights, comparing 4 different areas of my city. I want to calculate the probability of each of the 4 Areas being the tallest:

• Example: What is the probability of A1 being the tallest Area ?

All of the 4 areas have a normal distribution on their heights

Areas = A1, A2, A3, A4

A1 = Mean 180 with SD 7.2
A2 = Mean 178 with SD 7
A3 = Mean 176 with SD 9
A4 = Mean 182 with SD 8.4

I don't know now, how to go forward from here. I do know how to compare two Areas I saw an example here:

For example, if I wanted to know the probability of A1 being taller than A2, I would get the Normal distribution of the difference of $A1-A2$, like:

$$D = A1 - A2 = 180 - 178 = 2\quad\text{ ----- this for the mean}$$

And for the SD, I get $(7.2^2 + 7^2)^{0.5} = 10.041$

So using the distribution D with mean 2 and SD 10.041, I just calculate the cumulative distribution for D>0. But, how to do the same analysis for the 4 areas?

$$A1 > (A2\ \&\ A3\ \&\ A4)$$

Thank you.

I am performing a study on individuals heights, comparing 4 different areas of my city. I want to calculate the probability of a each of the 4 Areas being the tallest.

All of the 4 areas have a normal distribution on their heights

Areas = A1, A2, A3, A4

A1 = Mean 180 with SD 7.2
A2 = Mean 178 with SD 7
A3 = Mean 176 with SD 9
A4 = Mean 182 with SD 8.4

I don't know now, how to go forward from here. I do know how to compare two Areas:

For example, if I wanted to know the probability of A1 being taller than A2, I would get the Normal distribution of the difference of $A1-A2$, like:

$$D = A1 - A2 = 180 - 178 = 2\quad\text{ ----- this for the mean}$$

And for the SD, I get $(7.2^2 + 7^2)^{0.5} = 10.041$

So using the distribution D with mean 2 and SD 10.041, I just calculate the cumulative distribution for D>0. But, how to do the same analysis for the 4 areas?

$$A1 > (A2\ \&\ A3\ \&\ A4)$$

Thank you.

I am performing a study on individuals heights, comparing 4 different areas of my city. I want to calculate the probability of each of the 4 Areas being the tallest:

• Example: What is the probability of A1 being the tallest Area ?

All of the 4 areas have a normal distribution on their heights

Areas = A1, A2, A3, A4

A1 = Mean 180 with SD 7.2
A2 = Mean 178 with SD 7
A3 = Mean 176 with SD 9
A4 = Mean 182 with SD 8.4

I don't know now, how to go forward from here. I do know how to compare two Areas I saw an example here:

For example, if I wanted to know the probability of A1 being taller than A2, I would get the Normal distribution of the difference of $A1-A2$, like:

$$D = A1 - A2 = 180 - 178 = 2\quad\text{ ----- this for the mean}$$

And for the SD, I get $(7.2^2 + 7^2)^{0.5} = 10.041$

So using the distribution D with mean 2 and SD 10.041, I just calculate the cumulative distribution for D>0. But, how to do the same analysis for the 4 areas?

$$A1 > (A2\ \&\ A3\ \&\ A4)$$

Thank you.

I am performing a study on individuals heights, comparing 4 different areas of my city. I want to calculate the probability of a random selected person from one area being the tallest.

All of the 4 areas have a normal distribution on their heights

Areas = A1, A2, A3, A4

A1 = Mean 180 with SD 7.2
A2 = Mean 178 with SD 7
A3 = Mean 176 with SD 9
A4 = Mean 182 with SD 8.4

I don't know now, how to go forward from here. I do know how to compare two Areas:

For example, if I wanted to know the probability of a randomly selected person from A1 being taller than A2, I would get the Normal distribution of the difference of $A1-A2$, like:

$$D = A1 - A2 = 180 - 178 = 2\quad\text{ ----- this for the mean}$$

And for the SD, I get $(7.2^2 + 7^2)^{0.5} = 10.041$

So using the distribution D with mean 2 and SD 10.041, I just calculate the cumulative distribution for D>0. But, how to do the same analysis for the 4 areas?

$$A1 > (A2\ \&\ A3\ \&\ A4)$$

Thank you.

I am performing a study on individuals heights, comparing 4 different areas of my city. I want to calculate the probability of a each of the 4 Areas being the tallest.

All of the 4 areas have a normal distribution on their heights

Areas = A1, A2, A3, A4

A1 = Mean 180 with SD 7.2
A2 = Mean 178 with SD 7
A3 = Mean 176 with SD 9
A4 = Mean 182 with SD 8.4

I don't know now, how to go forward from here. I do know how to compare two Areas:

For example, if I wanted to know the probability of A1 being taller than A2, I would get the Normal distribution of the difference of $A1-A2$, like:

$$D = A1 - A2 = 180 - 178 = 2\quad\text{ ----- this for the mean}$$

And for the SD, I get $(7.2^2 + 7^2)^{0.5} = 10.041$

So using the distribution D with mean 2 and SD 10.041, I just calculate the cumulative distribution for D>0. But, how to do the same analysis for the 4 areas?

$$A1 > (A2\ \&\ A3\ \&\ A4)$$

Thank you.