Daily yield, CLT on a mean

Module E · freq 9

$\bar{X}\sim N\!\left(\mu,\frac{\sigma^2}{n}\right)\qquad \ell=\mu+z_{\alpha}\frac{\sigma}{\sqrt{n}}$

Signals: "average yield for a 31-day month falls below 20.2" · b) reverse question "trigger an investigation in only 4% of months, what should the lower limit be set to"

Knowledge point:Sampling distributions & CLT →

Generating question…

Method

a) stats.norm.cdf(20.2, mu, sigma/np.sqrt(n))
b) mu + stats.norm.ppf(0.04)*sigma/np.sqrt(n) (z is negative)
c) iid random sample

Pitfalls where marks are lost

Using √n·σ (that's for the sum) —— for the mean use σ/√n
b) using ppf(0.96) —— the lower limit is in the left tail, use ppf(0.04)