Question 1198619
mean = 4
standard deviation = 1


z-score formula is z = (x-m)/s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.


in your problem:
m = 4
s = 1


when x = 3.3, the formula becomes:
z = (3.3 - 4) / 1 = -.7
area to the left of z = -.7 = .2419635782.
area to the right of z = -.7 = 1 minus .2419635782 = .7580364128.


when x = 9, the formula becomes:
z = (9 - 4) / 1 = 5
area to the left of z = 5 = .9999997129.
area to the right of z = 5 = 1 - .9999997129 = .000000287195.


when 3.3 < x < 9, area between those 2 x-values is area to the left of z-score of 9 minus area to the left of z-score of -.7 = .9999997129 minus .2419635782 = .7580361347.


here's what those values look like on a graph.


<img src = "http://theo.x10hosting.com/2022/112701.jpg">


<img src = "http://theo.x10hosting.com/2022/112702.jpg">


<img src = "http://theo.x10hosting.com/2022/112703.jpg">


if i did this correctly, your solutions are:


(a) At least 3.3 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)


.7580


(b) At most 9 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)


.0000 = 0


(c) Between 3.3 percent and 9 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)


.7580