Beta probability (laboratory offers bottles of hydrogen peroxide...)

qqsszz

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A laboratory offers bottles of hydrogen peroxide of 100 cm3 with a deviation of 4 cm3 A random sample of 144 bottles is taken and it is found that the average volume is 101 cm3.
I have trouble with this: Find \(\displaystyle \beta\) for the case where the true average volume is 101.2 cm3
\(\displaystyle Z = \frac{100-101.2}{\frac{4}{12}} = -3.6\)
\(\displaystyle \beta = P(Z < -3.6)\)
Which is nearly 0
 
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