SOLUTION: I'm struggling with the part b of this question and will very greatly appreciate it if someone can help me with this answer . The pressure monitoring systems (TPMS)warns drivers

Question 1208488: I'm struggling with the part b of this question and will very greatly appreciate it if someone can help me with this answer .
The pressure monitoring systems (TPMS)warns drivers when tire pressure is 26% below target pressure. The target tire pressure of a certain car is 28 psi.
Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi, if the car's average tire pressure is on target , what is the probability that the TPMS will trigger a warning ?

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: 0.00755 (approximate)

Explanation

(1-0.26)*28 = 20.72 psi or smaller would be when the warning is signaled.

Compute the z score
z = (x-mu)/sigma
z = (20.72-28)/3
z = -2.426667 approximately
z = -2.43
Then use a Z table in the back section of your textbook.
If you don't have your textbook with you, then you can use a website like this one

Locate the row that starts with -2.4
Highlight the column that has 0.03 at the top.
The value 0.00755 is in this row and column.
This value is approximate.
We can say that P(Z < -2.43) = 0.00755 which is the approximate final answer in decimal form.

There's roughly a 0.755% chance that the TPMS will trigger a warning.

If you want to use technology, then you have a variety of options.

Search online for a specialized normalCDF calculator. There are many to choose from. This one is my favorite because it's very user friendly and draws a diagram. The only drawback is that it doesn't appear to have any option to set the rounding precision.
Use the NormalCDF function on a TI83 or similar.
Use the NormDist function in a spreadsheet.
Use the Normal command in GeoGebra.
There are many other apps that you can use as well (eg: WolframAlpha, Mathematica, StatDisk, etc).

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