Question 1201699
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Answer: <font color=red>64.15%</font> (approximate)


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Work Shown 


mu = 155 = population mean load time
sigma = 10 = population standard deviation of the loading times
x = load time in minutes


The task is to compute P(133 < x < 159) to find the percentage of load times between 133 minutes and 159 minutes.


Find the z score when x = 133
z = (x-mu)/sigma
z = (133-155)/10
z = -22/10
z = -2.20


Do the same for x = 159
z = (x-mu)/sigma
z = (159-155)/10
z = 4/10
z = 0.40


The task of finding P(133 < x < 159) is equivalent to P(-2.20 < z < 0.40)


I'll be using this Z table
<a href = "https://www.ztable.net/">https://www.ztable.net/</a>
That table in the link should resemble the table your teacher has provided.
On that link, scroll down the page to see a few examples how to read that table.


Use such a table to find that
P(Z < -2.20) = 0.01390
P(Z < 0.40) = 0.65542
So,
P(a < Z < b) = P(Z < b) - P(Z < a)
P(-2.20 < Z < 0.40) = P(Z < 0.40) - P(Z < -2.20)
P(-2.20 < Z < 0.40) = 0.65542 - 0.01390
P(-2.20 < Z < 0.40) = 0.64152
which leads back to
P(133 < x < 159) = 0.64152
This is the approximate probability of getting an x value between 133 and 159.


Convert that to a percentage
0.64152 --> 64.152%
That rounds to <font color=red>64.15%</font>


Approximately <font color=red>64.15%</font> of the load times are between 133 minutes and 159 minutes.


You could use a specialized stats calculator such as this one
<a href = "https://davidmlane.com/normal.html">https://davidmlane.com/normal.html</a>
as an alternative to using a Z table.


This article goes over a few examples of how to calculate normal distribution probabilities on a TI84 calculator.
<a href="https://www.statology.org/normal-probabilities-ti-84-calculator/">https://www.statology.org/normal-probabilities-ti-84-calculator/</a>


A spreadsheet is another option.
Unfortunately I'm not familiar with the ALEKS calculator.
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