The equation for a general normal curve with mean μ and standard deviation σ is
y =
e−(x − μ)2/(2σ2)
σ
2π
.
Calculate values for x = 20, 30,
, 70, 80 where μ = 50 and σ = 10. Note that setting
μ = 0
and
σ = 1
in this equation gives the equation for the standard normal curve. (Round your answers to four decimal places.)
I think you mean
if Z = 1 / sqrt(2 pi sigma^2)
then
y = Z e^-(x-u)^2/(2 sigma^2)
=========================
for example if sigma = 10 and u = 50
for x = 20
Z = 1/sqrt(2 pi *100) = 1/sqrt 628 = 1/25.1 = 0.0398
y = 0.0398 e^-[( 30^2)/(200)]
y = 0.0398 e^-[4.5]
y = 0.0398 * 0.111
y = 0.000442
check my arithmetic
To calculate the values for x = 20, 30, 70, and 80 using the formula for the general normal curve, we will plug in the given values of μ = 50 and σ = 10 into the equation:
y = e^(-(x - μ)^2 / (2σ^2)) / (σ * sqrt(2π))
For x = 20:
y = e^(-((20 - 50)^2) / (2 * (10^2))) / (10 * sqrt(2π))
= e^(-900 / 200) / (10 * sqrt(2π))
≈ 0.0005
For x = 30:
y = e^(-((30 - 50)^2) / (2 * (10^2))) / (10 * sqrt(2π))
= e^(-400 / 200) / (10 * sqrt(2π))
≈ 0.0063
For x = 70:
y = e^(-((70 - 50)^2) / (2 * (10^2))) / (10 * sqrt(2π))
= e^(-400 / 200) / (10 * sqrt(2π))
≈ 0.0063
For x = 80:
y = e^(-((80 - 50)^2) / (2 * (10^2))) / (10 * sqrt(2π))
= e^(-900 / 200) / (10 * sqrt(2π))
≈ 0.0005
So, the values for x = 20, 30, 70, and 80 with μ = 50 and σ = 10 are approximately 0.0005, 0.0063, 0.0063, and 0.0005 respectively.