Question 1134637
1. If P(-z < Z < z) = 0.5098, find z.


the area between -z and z is equal to .5098.


the z-score in the middle between -z and z is equal to 0.


the area to the left of a z-score of 0 is equal to .5.


the area between -z and 0 is half the area between 0 and z.


because the normal distribution is symmetric, take .5098 and divide it by 2 to get .2549.


the area to the left of 0 is equal to .5


the between -z and 0 is equal to .2549.


subtract .2549 from .5 to get .2451.


that's the area to the left of -z.


solve for -z to get -z = -.6899907576.


that makes z = .699907576.


that's your solution.


the area between -.6899907576 and .699907576 is equal to .5098001472 which is equal to .5098 when rounded to 4 decimal digits.


the solution is confirmed to be good.


visually it looks like this.


<img src = "http://theo.x10hosting.com/2019/021207.jpg" alt="$$$" >



2. Find P(-2.11 < Z < -0.37).


the area between -2.11 and -.37 is equal to .3382621848


i think that's what you're looking for.


if it isn't, let me know what it is that you're looking for here.


here's a visual display of what i think you are looking for.


you look up the area to the left of a z-score of -2.11 and you look up the area to the left of a z-score of -.37 and you subtract the smaller area from the larger area to get your anser.


using my calculator, i got the following:


area to the left of a z-score of -2.11 is equal to .0174291159


area to the left of a z-score of -.37 is equal to .3556913007


after between -2.11 and -.37 is equal to .3556913007 minus .0174291159 which is equal to .3382621848.


that's the same as i got before when i asked the calculator for the area between a z-score of -2.11 and -.37 directly.


the calculator i use is the TI-84 Plus to solve problems like these.


here's a visual display.


<img src = "http://theo.x10hosting.com/2019/021206.jpg" alt="$$$" >


let meknow if you have any questions or need further clarification on points you don't understand.