Question

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $47,000 and a standard deviation of $6,900. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)

(a) Find the 90th percentile for an individual teacher's salary. $ 55843

(b) Find the 90th percentile for the average teacher's salary.

If you can show me how to break this down on a TI-84, that would be great. I don't have a z or t table. Please don't tell me they are included with the book, because they are not included with mine and I need to know how to do this on a calculator as that is what my instructor wants. Part a is correct, I just can't figure out b.

Thanks in advance.

Answer 1

Since you are done with part a, I will be explaining you to find the 90th percentile for the average teacher's salary. Basically, we need to find P( < k) = 0.90 where we need to find the value of k. Basically we will use the inverse norm function on your calculator, usually we go forward when we have to calculate the probability but here we are provided with the probability and we need to find the value of k which means going backwards.

here they are asking us the 90th percentile for the average teacher's salary. so we will change the standard deviation for individual value to the standard deviation for sample means i.e. where = 6900 and n = 10.

now the s.d. = 2182 (after rounding off)

now using TI-84.

press the button 2nd on top left and then press the vars button on the right

There will appear different options and as i explained earlier we have to use the inversenorm function so after pressing 3 on your calculator, it will ask you to fill some details i.e. area which will be .9 in this case and mean will be 47000 and s.d. i.e. sigma will be 2182 (for the average) and then press paste and enter your answer will come out to be 49796 (after rounding off).