Question

Lee missed the lesson on normal distribution and needs to do his homework. Explain to Lee how to use the mean and standard deviation of a normal distribution to determine the top 6% of the population.

Answer 1

@kropot72

Answer 2

A standard normal distribution table can be used to find the top 6% of the population. First it is necessary to use the table to find the z-score that gives a cumulative probability of 1.00 - 0.06 = 0.94.
Can you do that step?

Answer 3

what step am I doing? looking for the z-score?

Answer 4

Yes. You need to use the table in reverse. There is a suitable table here:
http://www.math.bgu.ac.il/~ngur/Teaching/probability/normal.pdf
Look for a cumulative probability close to 0.940, and then find the corresponding value of z-score.

Answer 5

I have a table handy and it's 0.82639

Answer 6

What do I do have after that?

Answer 7

No, you did not use the table in reverse. You found the cumulative probability for a z-score of 0.940. We already have the cumulative probability, it is 0.9400. We need to find the z-score that gives such a value of cumulative probability.

Answer 8

I'm sorry but I don't understand. What's the reason for 0.82639?

Answer 9

Please wait 10 minutes. I am having a meal. 0.82639 does not have any use.

Answer 10

Lets try using the table in reverse to find the z-score that gives a cumulative probability of 0.5000. Can you do that ?

Answer 11

Sorry, my computer was acting weird

Answer 12

Ok

Answer 13

So in reverse. Would it be 1.55 because the closet I found was 0.93943

Answer 14

Yes that is the z-score for a cumulative probability of 0.9400. Next, to find the required value of the random variable X, we use the formula:
\[\large z=\frac{X-\mu}{\sigma}\]
giving
\[\large 1.55=\frac{X-\mu}{\sigma}\]

Answer 15

Now it is necessary to rearrange the equation to find X in terms of mu and sigma.

Answer 16

How do I found it?

Answer 17

this is confusing

Answer 18

\[\large X-\mu=1.55 \sigma\]
Therefore
\[X=1.55 \sigma+\mu\]

Answer 19

Ok. What Do I do? Am i plugging 0.6 in x?

Answer 20

Just forget it. I'm not really understanding and sorry for wasting your time. I'll give you a metal. Thank you

Answer 21

The solution is the equation for X.
Values of the variable above X are in the top 6% of the population. Just plug the values of the population mean (mu) and population standard deviation (sigma) into the equation:
\[\large X=1.55 \sigma + \mu\]