# The normal distribtuion?

• Jun 24th 2011, 11:58 AM
homeylova223
The normal distribtuion?
A set of data is normally distributed with a mean of 140 and a standard deviation of 20.

1. What percent of data is between 100 and 150?

2. Find the value that defines the 75th percentile.

I am having trouble figuring number one out because one is below the mean and the other one is above the mean? Is there a formula I can use a 150 is not part of stat deviation.
• Jun 24th 2011, 12:19 PM
FernandoRevilla
Re: The normal distribtuion?
Quote:

Originally Posted by homeylova223
I am having trouble figuring number one out because one is below the mean and the other one is above the mean? Is there a formula I can use a 150 is not part of stat deviation.

No problem, just routine. For example

$p(100\leq x\leq 150)=p\left(\dfrac{100-140}{20}\leq z\leq\dfrac{150-140}{20}\right)=\ldots$

Now use the table of the $N(0,1)$ distribution.
• Jun 24th 2011, 02:13 PM
homeylova223
Re: The normal distribtuion?
To find the percentile I found this formula online not in my text book

(75/100) (n+1) Will give me the percentile but what would I plug into n because this is normal distribution and not a set for example 99.7 percent of the data is three standard deviation from the mean. So what would I do?

Any help would be great.
• Jun 24th 2011, 05:16 PM
mr fantastic
Re: The normal distribtuion?
Quote:

Originally Posted by homeylova223
To find the percentile I found this formula online not in my text book

(75/100) (n+1) Will give me the percentile but what would I plug into n because this is normal distribution and not a set for example 99.7 percent of the data is three standard deviation from the mean. So what would I do?

Any help would be great.

You need to go to your class notes and or textbook and review the many examples that are sure to be there. You also need to arrange for one-on-one help from your instructor or a tutor because you have serious problems with this topic.

The formula you have found is not relevant to your question. It applies to discrete data.

The 75th percentile is given by the value of a such that Pr(X < a) = 0.75.

So find the value z* such that Pr(Z < z*) = 0.75.

Then use the fact that it follows from Z = (X - mean)/(standard deviation) that z* = (a - 140)/20. Solve for a.

If none of this makes sense, you need to re-read my first two lines. It is certain that youir textbook has examples that explain all this.