You know that 68% of the scores lies in the interval . So you know that Jim's score is .
I'm struggling with a stats problem....can anyone help me out. I don't just want an answer I want to know how to do the work.
Jimís score on a Stats Exam was 0.4 SD above the mean. What are the 2 possible z-scores Joe would need to obtain for the area under the curve between Jim and Joe to be 27%? Assume the Stats Exam is normally distributed. Show work.
Any help appreciated. Thanks!
Assume the standard normal distribution (i.e. ). Then Jims score is or . So I used a table and got one of the z-scores as . The other one was . The area is approx. .
So (we standardize the z-score). They ask for 2 possible z-scores because you can have a z-score greater than or less than such that the area is . We are using one of those z-score tables in the back of a stats book.
you can also use some of those online calculators that calculates z-scores. That is probably more accurate than tables. Google 'z-score calculators.'
Or Distribution Tables
The left hand numbers (bold ones) are the z scores, and the right hand numbers are the area to the left of the particular point. So I found the area and matched it with the z-score.
Notice that which is the the difference between the z-scores and in the table. So its not exact, but close enough.