Question 1197365
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mu = 1173 = population mean
sigma = 115 = population standard deviation


On a TI83 or TI84 calculator, you will type in the following
invNorm(0.3)
This function is found by pressing the key labelled "2nd" followed by the VARS key. The invNorm function is the third item.
The result is approximately -0.5244
Here's another calculator you can use
<a href = "https://davidmlane.com/normal.html">https://davidmlane.com/normal.html</a>
Alternatively, you can use the NORMINV function in a spreadsheet.


What this tells us is
P(Z < -0.5244) = 0.30 approximately
In other words, z = -0.5244 is the approximate 30th percentile critical z score.
About 30% of the area under the Z curve is to the left of z = -0.5244


Use this z score to find the corresponding x value
z = (x - mu)/sigma
z*sigma = x-mu
x = z*sigma + mu
x = -0.5244*115 + 1173
x = 1112.694
x = 1112.69


Answer: 1112.69
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