Using a TI-84 calculator to find the lowest 20% of a normal curve

Question

I am not the greatest at math, I am very confused about the second part of this problem, the problem is

Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5. Find the probability that a value is between 65 and 80 using your TI calculator.

Which I got was 0.8536

The second part of the questions is the troublesome part (for me at least) it asks

Using the same normal curve above, determine the value for which the lowest 20% of the data is under using your TI calculator

I have attached the graph being used

Answer 1

Comment. Six hours and no answer to what ought to be an easy question.

You are asking for the 20th percentile or quantile .2. This is found using the inverse CDF. I do not have a TI calculator at hand, but seem to recall there is a way to find inverse CDFs. From R statistical software the answer is 16.2127 because in R the normal inverse CDF function is called 'qnorm'. (This doesn't match the colored area in the picture you linked. I think that figure is for the first part of the problem.)

qnorm(.2, 70, 4.5)
##  66.2127

You can verify this is right by verifying the probability between $-\infty$ and 66.2127 is 0.20. Or that the probability between $-100$ and 66.2127 is o.20.

I hope this helps.

Maybe someone with a TI calculator will see this and tell you exactly how to do inverse CDFs on a TI. (I edited your Question to make it easier for the right person to find.) Also, I suppose you can google something like TI calculator inverse normal CDF and get help on the Internet.

This Answer on our site mentions an invNORM function on a TI-84. Maybe it will help.