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.
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.
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.