Question 1173064
the z-score with .9645 of the area under the normal distribution curve to the left of it would be z = 1.805477458.


this can be seen visually as shown below:


<img src = "http://theo.x10hosting.com/2021/011402.jpg" >


i used the ti-84 plus calculator to get the more detailed answer.


if you were to use the z-score normal distribution tables, you would do the following:


z-score of 1.80 has area of .96407 to the left of it.
z-score of 1.81 has area of .96485 to the left of it.
.96485 - .96407 = .00078
.96450 - .96407 = .00043
.00043 / .00078 = .5512820513 * .01 = .005512820513
1.80 + .005512820513 = 1.805512820513.


that's not exactly equal to 1.805477458, but it's pretty close.
it is less than .002% higher.
that's less than 2/1000th of a percent.


the reason is that the interpolation is a straight line interpolation, whereas the calculator is looking at the actual curve itself between the two z-scores, which is not a straight line.


regardless, both methods will get you an answer that is perfectly acceptable.
in fact, they are the same when rounded to 4 decimal places.


since you are asked to round to 3 decimal places, then your answer would be 1.805 either way.


your answer should be a z-score of 1.805 that has .9645 of the area under the normal distribution curve to the left of it.