SOLUTION: The number of chocolate chips in an 18-ounce bag of a particular brand of chocolate chip cookies is normally distributed with mean 1,173 chips and standard deviation 115 chips.

Question 1197365: The number of chocolate chips in an 18-ounce bag of a particular brand of chocolate chip cookies is normally distributed with mean 1,173 chips and standard deviation 115 chips.
Calculate the 30th percentile of the number of chocolate chips in an 18-ounce bag of these chocolate chip cookies. Give your answer as a decimal rounded to two digits after the decimal.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

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
https://davidmlane.com/normal.html
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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