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

1
by Giching

Log in to add a comment

by Giching

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

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.

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.