Question 1200165: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 6.9 days and standard deviation of 1.8 days. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent.
a) What is the probability of spending less than 9 days in recovery?
%
b) What is the probability of spending more than 4 days in recovery?
%
c) What is the probability of spending between 4 days and 9 days in recovery?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
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 normalcdf
The template is:
normalcdf(L, U, mu, sigma)
where,
L = lower boundary
U = upper boundary
mu = mean
sigma = standard devation
For part (a), you'll type in normalcdf(-9999,9,6.9,1.8)
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 normalcdf(0,9,6.9,1.8) to get 0.878264 which isn't too far off the previous result.
Either way, we arrive at a final answer of 87.8% 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: normalcdf(4,9999,6.9,1.8)
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 94.6%
Lastly for part (c) we have:
input = normalcdf(4,9,6.9,1.8)
output = 0.8247 approximately
That converts to 82.5%
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Summary Answers:
(a) 87.8%
(b) 94.6%
(c) 82.5%
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