Just want to make sure I'm doing this correctly
Question:
The weight limit of a scale is 5.25 kilograms. W is normally distributed with mean weight 5.15 kilograms and standard deviation $\sigma$. The probability that W exceeds the weight limit of the scale is 0.3228.
What is the value of the second moment?
Attempt:
$P(Z>\frac{5.25-5.15}{\sigma}) = .3228$
$P(Z<\frac{5.25-5.15}{\sigma}) = 1- .3228 = .6772$
$\frac{5.25-5.15}{\sigma} = .46$
$5.25-5.15 = .46\sigma$
$\sigma = \frac{.1}{.46} = .21739$
$\sigma^2 = .21739^2 = .04725$
$E(W^2) = \sigma^2 + (E(W))^2 = .0475 + 5.15^2$
$E(W^2) = 26.5697 \approx 26.570$