Question 1169546
the probability is .0107


i used the ti-84 plus calculaor.


there are several online calculators you can use that will provide the same answer to you.


one of the calculators that i use can be found at <a href = "https://www.calculator.net/z-score-calculator.html?c1raw=-2.3&c1mean=0&c1sd=1&calctype=zscore&x=66&y=25" target = "_blank">https://www.calculator.net/z-score-calculator.html?c1raw=-2.3&c1mean=0&c1sd=1&calctype=zscore&x=66&y=25</a>


the calculator can work off of z-scores or off of raw scores.


put in a mean of 460 and a standard deviation of 50 and a raw score of 345.
hit calculate and your answer shows up.


here's what it shows.


<img src = "http://theo.x10hosting.com/2020/111205.jpg">


the calculator tells you what the z-score is (-2.3)


you can calculate the z-score yourself by using the formula of:
z-score = (x-m)/s
x is the raw score
m is the mean
s is the standard deviation.
in your problem (x-m)/s becomes (345-460)/50 = -2.3


if you are using the z-score rather than the raw score, you would enter a mean of 0 and a standard deviation of 1 and give it the z-score instead of the raw score.


you would get the following results.


<img src = "http://theo.x10hosting.com/2020/111206.jpg">