Find P(11 < x < 16) when mu = 15 and sigma = 3. ?

Question

Find P(11 < x < 16) when mu = 15 and sigma = 3. ?

Answer 1

The probabilty density function in this case is

f(x) = 1/(3*sqrt(2*pi)) * e^[ - (x-15)^2/18 ]

P(11 &lt; x &lt; 16) ≈ ∫ 1/(3*sqrt(2*pi)) * e^[ - (x-15)^2/18 ] dx for x=11 to x=16

I used the Midpoint Rule to approximate this integral.

With n=10, my result is 0.53974673

With n=20, my result is 0.53944715

P(11 &lt; x &lt; 16) ≈ 54%