Question 1197052
<font color=black size=3>
The notation N(3468, 489) tells us we have a normal distribution with these parameters
mu = 3468 = mean
sigma = 489 = standard deviation


If a student got a scholarship, then they landed somewhere on this normal distribution. 
The majority of the students will cluster around the mean of $3468


Let's convert the raw score x = 4100 to its corresponding z score
z = (x - mu)/sigma
z = (4100 - 3468)/489
z = 1.29 approximately


Then we'll use a Z table such as this one
<a href = "https://www.ztable.net/">https://www.ztable.net/</a>
or one found in the back of your book.


That table says
P(Z < 1.29) = 0.90147
So about 90.147% of the students who got a scholarship received less than $4,100


If you were to use a calculator such as this one
<a href = "https://davidmlane.com/normal.html">https://davidmlane.com/normal.html</a>
then you'll find that P(Z < 1.29) = 0.9015
The area under the curve to the left of z = 1.29 is roughly 0.9015


Alternatively you can use a TI83 or TI84 calculator to type in <font color=blue>normalcdf(-99,1.29)</font> and it will display 0.9014746057 approximately. The normalcdf function can be found by hitting the key labeled "2nd" then pressing the VARS key.


If you wish to use a spreadsheet, then type in <font color=blue>=NORM.DIST(1.29,0,1,true)</font>
The 1.29 refers to the z score we calculated
the 0 and 1 are the mean and standard deviation respectively
The "true" tells the spreadsheet to compute the cdf rather than pdf
You could also type in <font color=blue>=NORM.DIST(4100,3468,489,true)</font> if you wanted to skip converting to a z score. This avoids the slight error that happens when we rounded the z score to 1.29


As you can see, there are various methods to calculating the area under the standard normal curve to the left of z = 1.29


-----------------------------------------------------------------


Answer: <font color=red>Approximately 90%</font> (when rounding to the nearest whole percent)
</font>