Scores on an exam are normally distributed with a standard deviation of 40 points. If a score of 552 place you exactly at the first quartile, find the
a. mean
b. median
c. IQR
d. mode
e. third quartile

Question

Scores on an exam are normally distributed with a standard deviation of 40 points. If a score of 552 place you exactly at the first quartile, find the
a. mean
b. median
c. IQR
d. mode
e. third quartile

anonymous · Answer

tbh, all I can't do is a and d. I think I can figure everything else out.

directrix · Answer

@Grazes  Do you know the z-score that corresponds to an area of .25 under the curve?

anonymous · Answer

I thought before that I needed the mean, but I change my mind. You would take .25 and convert it to the z value and put it in the equation$$z =\frac{ 552-\mu }{ 40 }$$
Right?
If it's right, how do I find the mode? :D

directrix · Answer

Correct except that you need the z value so that you can solve for the mean.

The z-score on the normal curve area chart or whatever you are using will have an associated area of .25 (first quartile).  Get that z and substitute it into what you already have and solve for the mean.

anonymous · Answer

Okay, how would I find the mode?

anonymous · Answer

I think if the graph is normally distributed then the mode is none, because all scores appear on the graph the same amount of times... once.

anonymous · Answer

mode is the the most frequently appearing number.

anonymous · Answer

Actually, the mode is usually the median and/or mean in a normal distribution, but I'm not sure which is the case.

anonymous · Answer

Ah. so then the mean median and mode are the same number.

anonymous · Answer

when a variable is normally distributed, the mean, median, and mode are the same number.