Statistics - Normal Distribution Question (scores)

[soupey]

I'm in a first year stats course and there is a question that I can't figure it out. Maybe I'm just tired, or perhaps I'm missing some basic concept. Here it is:

Suppose that the distribution of scores on an exam is closely described by a normal curve with mean 100. The 16th percentile of this distribution is 80.

a) What is the 84th percentile?
b) What is the approximate value of the standard deviation of exam scores?
c) What z score is associated with an exam score of 90?
d) What percentile corresponds to an exam score of 140?
e) Do you think there were many scores below 40? Explain.

I'm stuck on how to find the standard deviation. The 84th percentile should just be 20 from the max, if its a normal curve. It should start at 0, with a median of 100, and end at 200, so that means the 84th percentile would be 180...right?

Does that mean the standard deviation (50% + 34% = 84%) is 80?

Thanks in advance for any help

 

[JohnM]

The key to this problem is to figure out exactly what the standard deviation is, and it can be determined by:

mu = 100
16th pct = 80

which means that 16% of the scores are below 80.

Using the normal distribution table, we find that a z-score of -0.994 corresponds to the 16th percentile (16% of the area under the curve is below z = -0.994)

then we can find the std dev:

z = (x - mu) / s
-0.994 = (80 - 100) / s

solve for s, and then it should be pretty easy to answer all of the questions

 

[soupey]

thanks for the reply, i think i figured it out after....since the 18th percentile was 80, u can say that the 84th is 120, and from that the similarities line up with a typical empirical normal curve, so the std deviation is 20, and from there the rest of hte questions were pretty easy...

thanks again..