Question 1200165
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For this solution post, I'll assume you have a TI83 or TI84 calculator.


If you do not have a TI83 or TI84 calculator, then here is a free online alternative.
https://onlinestatbook.com/2/calculators/normal_dist.html
That calculator offers a nice diagram to go with the numeric result. That calculator also seems to be far more intuitive/user friendly.
The drawback is that there isn't an option to change the level of precision. Also, it's not allowed in many exam room settings. So that's why I'll go with the TI option in this solution post.



On the TI calculator, press the button labeled "2nd" in the top left corner.
Then press the VARS key to bring up the stats distribution menu.


Scroll down to <font color=blue>normalcdf</font>


The template is:
<font color=blue>normalcdf(L, U, mu, sigma)</font>
where,
L = lower boundary
U = upper boundary
mu = mean
sigma = standard devation


For part (a), you'll type in <font color=blue>normalcdf(-9999,9,6.9,1.8)</font>
The lower boundary L has -9999 to represent negative infinity. Simply pick any large negative number.
The TI calculator should produce a result of roughly 0.878327


Now you are hopefully thinking to yourself: "Why would the value of L be negative, when a negative number of days makes no sense?" 
That's a good point. So it might be practical to revise L into L = 0.
Type in <font color=blue>normalcdf(0,9,6.9,1.8)</font> to get 0.878264 which isn't too far off the previous result.


Either way, we arrive at a final answer of <font color=red>87.8%</font> when converting to a percentage and rounding to the nearest tenth of a percent.


For part (b), we'll have this input into the calculator: <font color=blue>normalcdf(4,9999,6.9,1.8)</font>
The 9999 represents positive infinity. Pick any other large value you want as long as it's beyond 3 standard deviations. 
The calculator should produce the result 0.9464 which then turns into <font color=red>94.6%</font>


Lastly for part (c) we have:
input = <font color=blue>normalcdf(4,9,6.9,1.8)</font>
output = 0.8247 approximately
That converts to <font color=red>82.5%</font>




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Summary Answers:
(a) <font color=red size=4>87.8%</font>
(b) <font color=red size=4>94.6%</font>
(c) <font color=red size=4>82.5%</font>
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