mean $792, standard dev $103; find limits of middle 50%

im following y what (i think) my book is telling me to do, but im really ocnfused, can someone please help me?

the average charitable contribution itemized per income tax return in pensylvania is $792. suppose that the distribution of the contribution is normal with a dtandard deviation of $103. Fin the limits for the middle 50% of contributions.

all of the examples in the book added .5000 to begin, so that's what i did, i can't figure out the reason why though. or maybe im just wrong...

.5000+.2500=.7500 (.68 is the closest on the chart to .7500)
(.68)(103)+792=862.04

.2500 (the closest on the chart is -.69)
(-.69)(103)+792=720.93

so th elimits are 720.93 and 862.04= is this the form i use= 720.93<x<862.04
maybe im reading to much into this, but that just doesn't seem correct, please help me

Limits for the middle 50%?. I suppose they are asking for 25% and 75%?.

Look up .75 in the body of the table and see what the corresponding z score is.

We see that is .675

\(\displaystyle .675=\frac{x-792}{103}\). This gives x=861.525

Do the same for 25%. Its corresponding z score is -.675

\(\displaystyle -.675=\frac{x-792}{103}\). x=722.475

I suppose that's what they mean. Maybe I misinterpreted. This is pretty close to what you have.

thank you so much!!!!, im still confused on how u came up with the .675 and -.675, i know it's the z score, but i can't find it in the table. i feel stupid :-(

Look up .75 in the BODY of the table. You have to interpolate in between .7486 and .7517. That is between .67 and .68. See now?.

Do the same for .25. No. you ain't stupid. When first introduced to these tables, they can be confusing.

ohhh, i see now! thannk you so i was just wrong to round .675 to .68? (that has to be what i did). or i didn't understand how to " interpolate in between " them. thank you for your help!

so am i right on this one?

an average price of a new home is $246,300... with a standard deviation of $15,000. find the min and max prices of the houses that a contractor would build to satisfy the middle 80% of the market. assume the variable is normally distributed.

so are they asking for 10 and 90 here? (or am i off there)?
if so would it be...
.9000=1.29 (do i have to interpolate in between to make it 1.285)???
.1000=-1.29 (or to interpolate in between to make it -1.285)????

is that even right? i want to learn this part correct before i go on...and thank you for your time and help.