# Find the area under the curve between 10 and 12 for a normal process with mean 6 and standard deviation 4.

1
by Giching

2015-09-29T15:16:17+05:30

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N(x) = normal distribution function.
Area under a normal process curve with σ>1, is same as the area under standard normal distribution curve σ=1 after conversion of the variable to standard normal variable.

The area values are available in a standard table.

Normal variable Z for the given variable values 10 and 12:
Z1 = (10 - 6)/4 = 1            Z2 = (12 - 6)/4 = 1.5

Area under curve between 10 and 12 :  F(Z2) - F(Z1)
= F(1.5) - F(1.0)
= 0.93319 - 0.84134
= 0.09185
it is 9.185% of the total area under the curve.

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