Discover Exam Mark Percentiles & Standard Deviation with Normal Curve

[BrownianMan]

Suppose that the distribution of marks on an exam is closely described by a normal curve with a mean of 65. The 84th percentile of this distribution is 75.
(a) What is the 16th percentile?
(b) What is the approximate value of the standard deviation of exam
marks?
(c) What z score is associated with an exam mark of 50?
(d) What percentile corresponds to an exam mark of 85?
(e) Do you think there were many marks below 35? Explain.

These are some exercises the prof gave us. That's all of the information given.

I'm having some difficulty getting started on a and b particularly.

 

[Mark44]

How does the 16th percentile compare to the 84th percentile? There is some symmetry you should be able to use.

Approximately how much of a normal distribution will be within 1 standard deviation of the mean?

 

[BrownianMan]

Ok, I attempted this again, and started by trying to find the standard deviation of the distribution. I got 10 for the st dev.

For the 16th percentile, I got 55%.

Is this correct?

 

[Mark44]

Yes, both seem correct to me.

 

[BrownianMan]

This is what I have:

a) 55

b) 10

c) -1.5

d) 98th percentile

e) No, not many are below 35, because 99.7% fall between 35 and 95.

Can anyone let me know if this is correct, or if I have made any errors?

Thanks.

 

[BrownianMan]

anyone?

 

[Mark44]

I won't guarantee that they're all correct, but they look fine. If you're off, you're not off by much. What would be helpful so that we don't also have to do this work, would be to include your supporting work.